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Topic: Lefschetz decomposition

Related Topics

Lefschetz fixed point theorem

Lefschetz number

Lefschetz decomposition

Lefschetz class

Lefschetz pencil

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	Lefschetz Decomposition for quotient varieties, by Reza Akhtar and Roy Joshua
		Lefschetz Decomposition for quotient varieties, by Reza Akhtar and Roy Joshua
		In an earlier paper, the authors had constructed an explicit Chow Kunneth decomposition for quotient varieties of Abelian varieties by actions of finite groups.
		In the present paper, the authors extend the techniques there to obtain an explicit Lefschetz decomposition for such quotient varieties for the Chow-Kunneth projectors constructed there.
	www.math.uiuc.edu /K-theory/0798 (72 words)

	Springer Online Reference Works
		Lefschetz' fixed-point theorem, or the Lefschetz–Hopf theorem, is a theorem that makes it possible to express the number of fixed points of a continuous mapping in terms of its Lefschetz number.
		The hard Lefschetz theorem is a theorem about the existence of a Lefschetz decomposition of the cohomology of a complex Kähler manifold into primitive components.
		The Lefschetz decomposition commutes with the Hodge decomposition (cf.
	eom.springer.de /l/l058000.htm (641 words)

	The Hard Lefschetz Theorem and the topology of semismall maps - de Cataldo, Migliorini (ResearchIndex)
		We prove that lef line bundles satisfy the Hard Lefschetz Theorem, the Lefschetz Decomposition and the Hodge-Riemann Bilinear Relations.
		We study proper holomorphic semismall maps from complex manifolds and prove that, for constant coecients, the Decomposition Theorem is equivalent to the...
		1 eme de Lefschetz et criteres de degenerescence de suites..
	citeseer.ist.psu.edu /410728.html (493 words)

	[No title]
		We have shown that this can be achieved for any closed oriented smooth 4-manifold X. To be precise, we can decompose X into two compact K\"ahler manifolds with strictly pseudoconvex boundaries, up to orientation, such that contact structures on the common boundary induced by the maximal complex distributions are isotopic.
		The decomposition gives rise to a folded K\"ahler structure on X, a globally defined 2-form, which is a particular generalization of a symplectic form.
		Moreover, folded Lefschetz fibrations, a certain analogue of Lefschetz fibrations, are shown to be the geometric counterpart of these structures.
	www.physsci.uci.edu /seminar/math/calendar.php?mode=abstract&id=824 (185 words)

	CMJ Contents: May 1998
		Examples are given for the family of tent maps, the logistic maps, and the quadratic maps associated with the Mandelbrot set.
		The authors show how the singular value decomposition (SVD) can be naturally introduced near the end of a typical elementary linear algebra course.
		For invertible matrices the SVD is equivalent to the polar decomposition, a decomposition that is easy to motivate and prove.
	www.maa.org /pubs/cmj_may98.html (1158 words)

	mypage (Site not responding. Last check: 2007-10-27)
		We consider a possibility of the existence of intersection homology morphism, which would be associated to a map of analytic varieties.
		We assume that the map is an inclusion of codimension one.
		For varieties with conical singularities we show, that the existence of intersection homology morphism is exactly equivalent to the validity of Hard Lefschetz Theorem for links.
	www.mimuw.edu.pl /~aweber/abs/ll9.html (94 words)

	Mark Goresky's Publications
		A decomposition theorem for the integral homology of a variety (with J. Carrell) Inv.
		Lefschetz fixed point formula for intersection homology (with R. MacPherson).
		Lefschetz numbers of Hecke correspondences (with R. MacPherson), in The Zeta Function of Picard Modular Surfaces, R. Langlands and D.
	www.math.ias.edu /~goresky/MathPubl.html (614 words)

	Gokova '00 (Site not responding. Last check: 2007-10-27)
		A useful tool to study Riemann surfaces (complex 1-manifolds) is their decomposition into pairs of pants.
		Each pair of pants is diffeomorphic to CP minus 3 points.
		The first interesting example is a decomposition of a quintic surface in CP (an irreducible 4-manifold) into 125 "pairs of pants".
	arf.math.metu.edu.tr /~gokova/2000 (335 words)

	teaching archive (Site not responding. Last check: 2007-10-27)
		The main goal is to overview some of the topological and geometric methods needed to study algebraic varieties and maps.
		This is the most general result known about the homology of maps between algebraic or Kaehler varieties.
		Line bundles/divisors/hypersurfaces, Bertini's Theorem, first Chern class, the Weak Lefschetz Theorem, the Kodaira Vanishing Theorem, pencils, monodromy, local systems.
	www.math.sunysb.edu /~mde/615S_03/615.html (236 words)

	7 Relation with cohomology
		The theorem of Lefschetz on (1, 1) classes asserts that the image of the cycle class map
		As we saw with zero cycles, the kernel of this homomorphism can be very large.
		On the other hand Bloch's conjecture asserts (in the case of zero cycles) that the kernel is torsion (hence zero by Roitman's theorem) in case the Hodge decomposition of
	www.imsc.res.in /~kapil/papers/harishconf/node8.html (528 words)

	Convex Polytopes and Toric Varieties: Gil Kalai and David Kazhdan (Site not responding. Last check: 2007-10-27)
		"The Hard Lefschetz theorem is known to hold for the intersection cohomology of the toric variety associated to a rational convex polytope.
		One can construct the intersection cohomology combinatorially from the polytope, hence it is well defined even for nonrational polytopes when there is no variety associated to it.
		Karu's paper is based on a construction by Barthel, Brasselet, Fieseler and Kaup and by Bressler and Lunts and also on a proof of "poincare duality" by Barthel, Brasselet, Fieseler and Kaup.
	www.ma.huji.ac.il /~kalai/polytopes.html (482 words)

	Course 18: Mathematics
		Basic subject on matrix theory and linear algebra, emphasizing topics useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, singular value decomposition, and positive definite matrices.
		Harmonic theory on complex manifolds, Hodge decomposition theorem, Hard Lefschetz theorem.
		Topics include direct and iterative methods for linear systems, eigenvalue decompositions and QR/SVD factorizations, stability and accuracy of numerical algorithms, the IEEE floating point standard, sparse and structured matrices, preconditioning, linear algebra software.
	student.mit.edu /catalog/m18a.html (4023 words)

	[No title] (Site not responding. Last check: 2007-10-27)
		This gives a new proof of the Normalization Theorem: If f:X --->X is a selfmap of a polyhedron, then I(f) equals the Lefschetz number of f.
		This result is equivalent to the Lefschetz-Hopf Theorem: If f: X --->X is a selfmap of a finite simplicial complex with a finite number of fixed points, each lying in a maximal simplex, then the Lefschetz number of f is the sum of the indices of all the fixed points of f.
		This is done by interpreting the $G$-homotopy classes in terms of the generalized fixed point transfer and making use of conormal maps.
	www.lehigh.edu /~dmd1/h3104.txt (1977 words)

	[math/0102116] Infinitesimal Variation of Harmonic Forms and Lefschetz Decomposition
		Title: Infinitesimal Variation of Harmonic Forms and Lefschetz Decomposition
		Abstract: This paper studies the infinitesimal variation of the Lefschetz decomposition associated with a compatible sl_2-representation on a graded algebra.
		This allows to prove that the Jordan-Lefschetz property holds infinitesimally for the Kaehler Lie algebra (introduced by Looijenga and Lunts) of any compact Kaehler manifold.
	www.arxiv.org /abs/math.AG/0102116 (114 words)

	Geometry / Topology Seminars
		A topological construction of a surface bundle with non-zero signature via a method of subtructing Lefschetz fibrations, Part II
		Open book decompositions and contact structures on 3-manifolds as an analog of Lefschetz fibrations and symplectic structures on 4-manifolds
		There is a tight connection between the multiplicities of modules appearing in the decomposition of M as an F
	www.math.metu.edu.tr /~gt/geomtopsem.html (1045 words)

	[No title] (Site not responding. Last check: 2007-10-27)
		Abstract: `Stein-cork decomposition' and `Lefschetz fibrations' are our main techniques to study smooth structures of 4-manifolds, but in practice every example requires its own bag of tricks.
		We will demonstrate this on Cappell-Shaneson's celebrated example: In 1987 they had proposed a possible counterexample to 4-dimensional Poincare Conjecture by constructing a possible nonstandard s-cobordism H* from S^3 to itself.
		We reduce the triviality of H to a question about the 3-twist spun trefoil knot in S^4, and also relate this to a question about a Fintushel-Stern knot surgery.
	www.math.wisc.edu /~xxchen/abstracts/akbulut.html (128 words)

	UT - math Calendar
		In the previous two talks, we looked at the extra structure of differential forms on a complex manifold, and also at Kaehler metrics on a complex manifold.
		This is the famous Hodge decomposition, and it provides (among other things) a topological obstruction to a complex manifold being Kaehler.
		If we have enough time, I'll also introduce the Lefschetz decomposition, which is guaranteed to make you smile.
	www.ma.utexas.edu /cgi-pub/seminar/calendar?year=2003&month=12&day=02 (590 words)

	[No title] (Site not responding. Last check: 2007-10-27)
		This paper studies the infinitesimal variation of the Lefschetz decomposition associated with a compatible sl_2-representation on a graded algebra.
		This allows to prove that the Jordan-Lefschetz property holds infinitesimally for the Kaehler Lie algebra (introduced by Looijenga and Lunts) of any compact Kaehler manifold.
		As a second application we describe how the space of harmonic forms changes when a Ricci-flat Kaehler form is deformed infinitesimally.
	celestial.eprints.org /cgi-bin/oaia2/arXiv.org?verb=GetRecord&identifier=oai:arXiv.org:math/0102116&metadataPrefix=oai_dc (73 words)

	Topology II - Final Exam
		Compute explicitly this homology sequence (the terms and the maps), in case the coefficients sequence is
		Compute the Lefschetz number L(f) in terms of the entries of A.
		Let X be a finite simplicial complex, and let G be a finite group acting simplicially on X.
	www.math.neu.edu:16080 /~suciu/mth3107/top2.final99 (177 words)

	On the handlebody decomposition associated to a Lefschetz fibration., A. Kas
		On the handlebody decomposition associated to a Lefschetz fibration., A. Kas
		On the handlebody decomposition associated to a Lefschetz fibration.
		[7] R. Mandelbaum, Special handlebody decompositions of simply connected algebraic surfaces, to appear.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.pjm/1102779371 (163 words)

	Evelyn Hart (Site not responding. Last check: 2007-10-27)
		On the occurrence of F(n) in the Zeckendorf decomposition of nF(n), joint with Laura Sanchis, Fibonacci Quarterly, 37 (1999), 21-33.
		A generalized Lefschetz number for local Nielsen fixed point theory, joint with J. Fares, Topology and its Applications 59 (1994) 1-23.
		Summer 2003: Wei Ren (Colgate `04) programmed for me using Magma so that I can study algebraically Nielsen fixed point theory on the wedge of two circles.
	math.colgate.edu /faculty/ehart.html (478 words)

	Complex geometry (Site not responding. Last check: 2007-10-27)
		The first half of the course will be an introduction to the basic techniques and results of complex manifold theory.
		Starting with rudiments of complex analysis in several variables, we will eventually learn about the Dolbeault theorem, Hermitian differential geometry, the Hodge theorem, Lefschetz decomposition, Kodaira's vanishing theorem and Kodaira's embedding theorem.
		We will then focus on compact Kähler surfaces which are complex surfaces admitting a Hermitian metric such that the corresponding (1,1) form is d-closed.
	www.imf.au.dk /da/uddannelse/beskrivelser/older/E1998/node19.html (159 words)

	Citebase - Lefschetz decomposition and the cd-index of fans
		The goal of this article is to give a Lefschetz type decomposition for the cd-index of a complete fan.
		follows from the Lefschetz decomposition of the cohomology.
		We give an analogue of the Lefschetz operation for the cd-index.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0509220 (164 words)

	[No title] (Site not responding. Last check: 2007-10-27)
		I will try to give a flavor of the results which are concerned with the structure induced on the cohomology H*(X,Q) of a projective manifold X by a projective map f: X --> Y. In particular:
		- we decompose H(X,Q) as a double direct sum of Hodge structures polarized by the intersection form on X (this generalizes the Primitive Lefschetz* Decomposition and the Hodge-Riemann Bilinear Relations),
		These results imply directly a refined version of the Decomposition Theorem of Beilinson, Bernstein, Deligne and Gabber for arbitrary proper algebraic maps.
	www.math.columbia.edu /~thaddeus/abstracts/decataldo03.html (145 words)

	GAEL - Géometrie Algébrique En Liberté
		This orbifold correction allows to construct in a very natural way a birational decomposition for a complex projective variety
		The course will be devoted to Hodge theory on compact Kähler and complex projective manifolds.
		We shall introduce the following essential notions and their basic properties: (polarised) Hodge structure, mixed Hodge structure, Hodge and Lefschetz decomposition.
	euclid.mathematik.uni-kl.de /~gael/current/programme/programme.html (528 words)

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