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Topic: Hyperplane section

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	[No title] (Site not responding. Last check: 2007-10-20)
		In section \class, we recall the basic results of the theory of integral closure of ideals and their application to the equisingularity theory of families of hypersurfaces with isolated singularities.
		In section {\sid}, we discuss the upper semi--continuity properties of the Segre numbers, and the behavior of the polar varieties of $I(t)$ in a family.
		Consider a hyperplane $H$ on $B$ induced by a hyperplane $H'$ in $\PP^{M-1}.$ An equation of $H'$ corresponds to a linear combination $g$ of the generators of $I.$ Suppose that $H$ is general w.r.t.
	home.imf.au.dk /esn/preprints/032 (7558 words)

	[No title]
		In Section 5 we show that the process starting with the hyperplane converges to an invariant measure with the same slope as the hyperplane and that under this invariant measure, the fluctuations between the heights at distant sites behave as in (\ref{eq:vem}).
		In Section 6 we discuss the one dimensional case and show that, when the initial distribution of heights differences is an ergodic stationary process with fluctuations, these fluctuations appear in the variance of the height at the origin when the process is biased.
		In Section 7 we discuss the passage from the discrete to the continuous case and in Section 8 we discuss the hydrodynamic limit.
	www.ma.utexas.edu /mp_arc/papers/97-198 (5531 words)

	Internal and external curvatures
		The sections of space-time by space-like hyperplanes allow to formulate the Hamiltonian formalism for integration of dynamical equations.
		The last will be understood as the splitting of 4-dimensional metric manifold on 3-dimensional space sections, which evaluates in the course of time.
		The relative position of these sections is defined by the "rigid" lines connecting the hyperplanes in the different space points (in the Fig.
	blake.prohosting.com /kalashni/examples/in_ex_curv_amaya.html (739 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		Beside another proof of one part of the correct semi-classical behaviour of the Berezin-Toeplitz quantization scheme, the asymptotic expansion of the pull-back of the Fubini-Study form of the projective space in which the manifold is embedded using the global holomorphic sections of the $m$-th tensor power of the quantum line bundle for $m\to\infty$ is identified.
		It is possible to study dynamics by considering operators on the collection of quantum Hilbert spaces given by the space of global holomorphic sections of the quantum line bundle and its tensor powers.
		This section is called the coherent vector associated to the point $\alpha$.
	www.math.uni-mannheim.de /~schlich/preprints/bolo.tex (5639 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		Note that for the projective space with quantum line bundle the hyperplane section bundle $H$, the bundle $U$ is just the tautological bundle.
		Sections of $L^m=U^{-m}$ can be identified with functions $\phi$ on $Q$ which satisfy the equivariance condition $\phi(c\la)=c^m\phi(\la)$.
		\end{proof} \begin{proof} (\refP{pari}) Recall that the identification of the sections of $L^m$ with equivariant functions on the circle bundle $Q$ is an isomorphy.
	www.math.uni-mannheim.de /~schlich/preprints/deform.tex (5441 words)

	basis (Site not responding. Last check: 2007-10-20)
		Abstract: We use the theory of hyperplane arrangements to construct natural bases for the homology of partition lattices of types A, B and D. This extends and explains the "splitting basis'' for the homology of the partition lattice given in a 1986 paper of the second author.
		Let $A$ be a central and essential hyperplane arrangement in $\Bbb R^d$.
		Let $R_1,...,R_k$ be the bounded regions of a generic hyperplane section of $A$.
	www.math.miami.edu /~wachs/abstracts/basis.html (139 words)

	commalg.org - the center for commutative algebra
		We obtain a characterization of the degree matrices that can occur for points in the plane that are the general hyperplane section of a non arithmetically Cohen-Macaulay curve of P^3.
		We prove that almost all the degree matrices with positive subdiagonal that occur for the general plane section of a non arithmetically Cohen-Macaulay curve of P^3, arise also as degree matrices of the general plane section of some smooth, integral, non arithmetically Cohen-Macaulay curve, and we characterize the exceptions.
		We also show that the matrices that arise as degree matrix of the general plane section of an arithmetically Buchsbaum, integral, (smooth) non arithmetically Cohen-Macaulay space curve are exactly those that arise as degree matrix of the general plane section of an arithmetically Buchsbaum, non arithmetically Cohen-Macaulay space curve and have positive subdiagonal.
	www.commalg.org /preprints/2003_09.shtml (1822 words)

	Science Fair Projects - Ample vector bundle
		In mathematics, in algebraic geometry or the theory of complex manifolds, a very ample line bundle L is one with enough sections to set up an embedding of its base variety or manifold M into projective space.
		These definitions make sense for the underlying divisors (Cartier divisors) D; an ample D is one for which nD moves in a large enough linear system.
		The relationship with projective space is that the D for a very ample L will correspond to the hyperplane sections (intersection with some hyperplane) of the embedded M.
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Ample_vector_bundle (419 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		In short, in Section 2, we formulate the autoduality theorem, our main result: if the curves in a family have double points at worst, then the Abel map $A_\cL^*$ is an isomorphism.
		In Section 3, we generalize Mumford's scheme-theoretic theorem of the cube, and conclude that $A_\cL^*$ is independent of the choice of $\cL$.
		Consider a {\it flat projective family of integral curves} $p\:C\to S$; that is, $S$ is a locally Noetherian scheme, and $p$ is a flat and projective map with geometrically integral fibers of dimension 1.
	www.mathnet.or.kr /preprint/impa/autoduality.tex (5204 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		We begin with a section describing notation for all the singularities we encounter (in which we follow Arnold fairly closely) and also a method for recognising each singularity when it presents itself in an equation not in normal form.
		This is followed by a short section discussing the relation between singularities on a hypersurface of degree $n$ with a singular point of multiplicity $n-1$ or $n-2$ and those of varieties obtained by projection.
		We recall notation from that section: \[F(w,x,y,z) = w^{2}z^{2} + 2wa(x,y,z) + b(x,y,z),\] where $a$ is divisible by $z$ and, as before, the terms divisible by $z^{2}$ can be removed by a substitution so we may write $a(x,y,z)=zp(x,y)$.
	home.imf.au.dk /esn/preprints/006 (14107 words)

	Algebra-seminar: Abstracts (Site not responding. Last check: 2007-10-20)
		We compare the geometry of an ample section of a projective variety with the geometry of the variety itself by the way of Mori theory.
		We apply this result to the case in which the section is a surface with Kodaira dimension $0$ or $1$, and to the case in which the section is a Fano manifold $($of high index$)$.
		I show how to apply this to the specific (open) problem of classifying Enriques-Fano threefolds (that is a threefold whose general hyperplane section of is an Enriques surface), and to the case of threefolds whose hyperplane sections are pluricanonical embeddings of surfaces of general type.
	www.math.uio.no /~ingerbo/algsem2/abstracts2.html (1176 words)

	Talks
		We show that the Euler obstruction of a complex analytic singularity is obtained from the Euler obstructions of the singularities of a general hyperplane section passing near the singularity.
		This result is established in the spirit of the Lefschetz Theorem on hyperplane sections.
		Dubson, M. Kato and R. Piene, which states that the Euler obstruction of a hypersurface of dimension d with an isolated singularity equals 1 + (-1)^{d-1} \mu^{(d-1)}, where \mu^{(d-1)} is the Milnor number of a generic hyperplane section through the singularity.
	math.univ-lille1.fr /~tibar/Sing/talks.htm (1004 words)

	Elisa's publications page - Keep reading!
		Here I address the question of lifting the property of being standard determinantal from the general hyperplane section of a scheme to the scheme itself.
		I produce examples of schemes of any dimension bigger than or equal to 2 and of codimension 3, such that the scheme is not standard determinantal, but its general hyperplane section is even good determinantal.
		Moreover, I show that if a scheme V of codimension 3 has one section Z by a hyperplane H that meets V properly, such that Z is good determinantal, then the general hyperplane section of V is good determinantal.
	www.math.unizh.ch /user/elisa/papers.html (735 words)

	Singular 2-0-5 Manual: Gauss-Manin connection
		The monodromy operator is the action of a positively oriented generator of the fundamental group of the puctured disc on the Milnor fibre.
		Sections in the cohomology bundle of moderate growth at
		: such a hypersurface has a smooth hyperplane section, and the complement is a small deformation of a cone over this hyperplane section.
	web.mit.edu /singular_v2.0.5/distrib/Singular/2-0-5/html/sing_378.htm (532 words)

	Title page for ETD etd-04092004-192242 (Site not responding. Last check: 2007-10-20)
		the plane that are the general plane section of a non arithmetically Cohen-Macaulay curve of P^3.
		determinantal from the general hyperplane section of a scheme to the scheme itself.
		a general hyperplane section of the scheme is good determinantal.
	etd.nd.edu /ETD-db/theses/available/etd-04092004-192242 (361 words)

	Transactions of the American Mathematical Society (Site not responding. Last check: 2007-10-20)
		Abstract: In this paper we establish a theorem which determines the invariants of a general hyperplane section of a rational normal scroll of arbitrary dimension.
		A general hyperplane section of this surface is a tetragonal curve; we use the first theorem to determine for which tetragonal invariants such a construction is possible.
		Finally we determine for which additional sets of invariants this construction gives a tetragonal curve as a hyperplane section of a singular canonically trivial surface, and discuss the connection with other recent results on canonically trivial surfaces.
	www.ams.org /tran/1997-349-08/S0002-9947-97-01811-4/home.html (272 words)

	What We Know About the Second Adjunction Mapping - Sommese (ResearchIndex) (Site not responding. Last check: 2007-10-20)
		Assume that n := dim b X 3 and let b L denote the restriction of the hyperplane section bundle O P N(1) to b X.
		The meromorphic map b \Phi k associated to jk(K b X + (n \Gamma 2) b L)j for k 1 ties together the pluricanonical maps of the surface sections of b X.
		5 the minimality of hyperplane sections of projective threefol..
	citeseer.ist.psu.edu /sommese97what.html (646 words)

	[No title]
		The part 1 of the theorem was proved (in a slightly weaker form) by Zhang (\cite{Zh}) and, in the case $E$ is spanned by global sections, by Wisniewski (\cite{Wi2}).
		Since $\f_{F(p)_x}: F(p)_x\ra F_i$ is generically unramified then choosing generic sections $A_i\in A$ yields that $p^{-1}(x) \cap F(\f)_{v_i}$ is a reduced cycle of length $d_i$ for any $i$ and $\sum_i d_i=d$.
		In fact take a general hyperplane section $A$ of $W$, and $X^{\prime}=\pi^{-1}(A)$ then $\pi_{X^{\prime}}:X^{\prime}\ra A$ is again a contraction supported by $K_{X^{\prime}}+det E_{X^{\prime}}$, such that $r\geq ((n-1)+1)/2$.
	alpha.science.unitn.it /~andreatt/preprint/tre10 (5365 words)

	Reducible hyperplane sections, II., M.C. Beltrametti, K.A. Chandler, A.J. Sommese
		In the case in which $\hatL$ is the union of $r \geq 2$ smooth normal crossing divisors, each of sectional genus zero, classification theorems were given for $\dim \hatX \geq 5$ or $\dim X=4$ and $r=2$.
		This paper restricts attention to the case of two divisors on a threefold, whose sum is ample, and which meet transversely in a smooth curve of genus at least $2$.
		Next, we give results on the case of a projective threefold $\hatX$ with hyperplane section $\hatL$ that is the union of two transverse divisors, each of which is either $\pn 2$, a Hirzebruch surface $\eff_r$, or $\widetilde{\eff_2}$.
	projecteuclid.org /Dienst/UI/1.0/Display/euclid.kmj/1071674437 (273 words)

	[No title]
		Choose a smooth hyperplane section $i:Z\hookrightarrow Y$ such that $h:=f_{Z}:Z\longrightarrow S$ is surjective and generically finite.
		Also we assume $Z \subset Y$ is a sufficiently general smooth hyperplane section of $Y$ that dominates $S$.
		Take the projectors $p_0(Y),...,p_6(Y)$ as defined in the last section.\\ To define the projectors for $X$, consider the graph $\Gamma_\varphi \subset Y \times X$ of $\varphi$.
	www.uni-essen.de /~mat903/preprints/3fold.tex (3091 words)

	[No title]
		The particular position of the singular points on $X$ --that is a consequence of the symmetries of the Chebyshev polynomials-- allows the presence of a divisor on the threefold through the nodes and not homologous to a multiple of a generic hyperplane section.
		The defect computes the number of independent divisors on the threefold through the nodes and not homologous to a multiple of a generic hyperplane section.
		In this section we explain how one may use this to find candidates for the local $L$-factors at the bad primes.
	www.math.ias.edu /preprints/katia/0009134.tex (13579 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		Instead, we consider the intersection of $\calV'$ with a hyperplane corresponding to a {cross}.
		The hyperplane section is defined by a certain ideal $\gota\subset\cz[Y_0,\dots,Y_9]$.
		These are rational functions on the moduli space of marked cubic surfaces that encode the manner in which the 27 lines on a cubic surface lie in $P^3$.
	www.ma.utexas.edu /~allcock/research/forms.tex (10130 words)

	3.1.1 Complexity of inducing oblique decision trees (Site not responding. Last check: 2007-10-20)
		An optimal hyperplane will minimize the impurity measure used; e.g., impurity might be measured by the total number of examples mis-classified.
		Intuitively, the problem is that it is impractical to enumerate all distinct hyperplanes and choose the best, as is done in axis-parallel decision trees.
		On the other hand, it is possible to define impurity measures for which the problem of finding optimal hyperplanes can be solved in polynomial time.
	www.tigr.org /~salzberg/murthy_thesis/node9.html (894 words)

	IRMA Strasbourg (Site not responding. Last check: 2007-10-20)
		In the special case where $\Gamma$ is the fundamental group of a Riemannian manifold of negative sectional curvature, $\overline{G}$ is the unit tangent bundle of the manifold equipped with the usual geodesic flow.
		In this paper, we construct, for every hyperbolic group $\Gamma$, a subshift of finite type and a continuous map from the suspension of this subshift onto $\overline {G}(\Gamma)$, which is uniformly bounded-to-one and which sends each orbit of the suspension flow onto an orbit of the geodesic flow.
		In the first sections we give the definitions and some properties of stable curves and maps, their moduli spaces, and virtual fundamental classes and Gromov--Witten invariants (following the constructions of Behrend and Fantechi).
	www-irma.u-strasbg.fr /irma/publications/1999/resum1999.shtml (6414 words)

	IngentaConnect Hyperplane Sections of Kantors Unitary Ovoids (Site not responding. Last check: 2007-10-20)
		The hyperplane sections of this variety and their stabilizers in the group G are determined.
		When q\equiv 2 (mod 3) one such hyperplane section is a member of the family of Kantor's unitary ovoids.
		We further determine all sections \Bbb{P}\Bbb{G}(D)\cap \mathcal{V} where D has codimension two in M and demonstrate that these are never empty.
	www.ingentaconnect.com /content/klu/desi/2001/00000023/00000002/00333265 (163 words)

	Classification Theory of Polarised Varieties - Cambridge University Press
		Using techniques from abstract algebraic geometry that have been developed over recent decades, Professor Fujita develops classification theories of such pairs using invariants that are polarised higher-dimensional versions of the genus of algebraic curves.
		The heart of the book is the theory of D-genus and sectional genus developed by the author, but numerous related topics are discussed or surveyed.
		Proofs are given in full in the central part of the development, but background and technical results are sometimes just sketched when the details are not essential for understanding the key ideas.
	www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0521392020 (245 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		If we think of the $C$ as embedded inside $\pp^2$, and let $H_2$ be the hyperplane section there, with $H_1$ the hyperplane section on the $\pp^1$, then these calculations are easy.
		But what in the ambient bundle gives a hyperplane section when restricted to $E$.
		Well if $H$ is a hyperplane containing the vertex we are blowing up at, then $\tilde{H}$ (the proper transform of $H$) restricts to a hyperplane section on $E$.
	www.math.fsu.edu /~wadams/diff_paper1.tex (6131 words)

	DC MetaData for: An Analytic Solution to the Busemann-Petty Problem on Sections of Convex Bodies (Site not responding. Last check: 2007-10-20)
		Abstract: We derive a formula connecting the derivatives of parallel section
		the ($(n-1)$-dimensional) volume of each central hyperplane section
		of $K$ is smaller than the volume of the corresponding section
	www.esi.ac.at /Preprint-shadows/esi693.html (227 words)

	Ein neuer Zusammenhang zwischen einfachen Gruppen und einfachen Singularitaeten (Site not responding. Last check: 2007-10-20)
		Then P contains exactly one closed orbit, a certain flag variety X. Using the killing form, every non-zero x in g defines a hyperplane in P, hence a hyperplane section X_x of X. Theorem: Assume x is regular nilpotent.
		This singularity is simple with the same Dynkin diagram as G. Furthermore, "perturbing x" is a versal deformation of the singularity.
		There is a paper dealing with hyperplane sections of X when V is an arbitrary simple G-module.
	www.math.rutgers.edu /~knop/papers/einf.html (206 words)

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