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	Invertible sheaf - Wikipedia, the free encyclopedia
		The invertible sheaves in those theories are in effect the line bundles appropriately formulated.
		In fact, the abstract definition in scheme theory of invertible sheaf can be replaced by the condition of being locally free, of rank 1.
		The direct construction of invertible sheaves by means of data on X leads to the concept of Cartier divisor.
	en.wikipedia.org /wiki/Invertible_sheaf (246 words)

	PlanetMath: line bundle
		In algebraic geometry, the term line bundle refers to a locally free coherent sheaf of rank 1, also called an invertible sheaf.
		sheaf of holomorphic sections is locally free and of rank 1.
		Cross-references: stalk, map, obvious, dimension, continuous functions, topology, sections, holomorphic, sheaf, variety, algebraic, non-singular, equivalent, vector bundle, complex, real, theory, manifold, invertible sheaf, rank, coherent sheaf, locally free, term, algebraic geometry
	planetmath.org /encyclopedia/LineBundle.html (136 words)

	Articles - Coherent sheaf (Site not responding. Last check: 2007-09-16)
		In mathematics, especially in algebraic geometry and the theory of complex manifolds, a coherent sheaf F on a locally ringed space X is a sheaf isomorphic with the cokernel of a morphism of O
		For a sheaf of rings R, a sheaf F of R-modules is said to be quasi-coherent if it has a local presentation, i.e.
		In the basic work of Serre, it was shown first that compact complex manifolds have the property that their sheaf cohomology for any coherent sheaf consists of vector spaces of finite dimension.
	www.techize.com /articles/Coherent_sheaf (677 words)

	PlanetMath: invertible sheaf
		A sheaf is invertible if and only if it is locally free of rank 1, and its inverse is the sheaf
		The set of invertible sheaves obviously form an abelian group under tensor multiplication, called the Picard group of
		This is version 3 of invertible sheaf, born on 2003-08-19, modified 2003-09-16.
	planetmath.org /encyclopedia/InvertibleSheaf.html (82 words)

	Invertible sheaf - Encyclopedia Glossary Meaning Explanation Invertible sheaf (Site not responding. Last check: 2007-09-16)
		Invertible sheaf - Encyclopedia Glossary Meaning Explanation Invertible sheaf.
		Here you will find more informations about Invertible sheaf.
		The orginal Invertible sheaf article can be editet
	www.encyclopedia-glossary.com /en/Invertible-sheaf.html (296 words)

	Abstract from Pacific Journal of Mathematics - 202-2-4 - Marc Coppens
		Let $X$ be a smooth projective variety, let $L$ be a very ample invertible sheaf on $X$ and assume $N+1=\dim(H^0(X,L))$, the dimension of the space of global sections of $L$.
		Consider the invertible sheaf $M:=\pi^*(L)\ot O_Y(-E_1 -\ldots-E_t)$ on $Y$.
		Using the same method of proof we obtain very sharp result for $K3$-surface and let $L$ be a very ample invertible sheaf on $X$ satisfying Cliff$\,(L)\geq 3$ (``most'' invertible sheaves on $X$ satisfy that property on the Clifford index), then $M$ is very ample if $t\leq N-5$.
	math.albany.edu:8000 /PacJ/2002/202-2-4nf.htm (281 words)

	Rec Fresh : Article 'Linear system of divisors' (Site not responding. Last check: 2007-09-16)
		The effect of working on varieties with singular points is to show up a difference between Weil divisors (in the free abelian group generated by codimension-one subvarieties), and Cartier divisors coming from sections of invertible sheaves.
		Linear systems are still at the heart of contemporary algebraic geometry; but they are typically introduced by means of the ample line bundle language.
		That is, the language of sheaf theory is considered the most natural starting point, at least to learn the theory.
	www.rec-fresh.net /DisplayArticleFull1029178.html (587 words)

	[No title]
		Proposition 2.11.The sheaf E(X) is a sheaf of analytic OC-algebras, which is in* *dependent up_to_canonical isomorphism of the choice of adapted open cover.
		In the case th* at V is spin, we give an explicit cocycle which exhibits E(V) as an invertible* sheaf of E(X)-modules.
		The formula (2.15)for this sheaf shows that such a global section is asse* mbled from sections a 2 E(X)a(Ua) which satisfy the formula b= ob-ae(a; b): (5.2) on U Ua\ Ub.
	hopf.math.purdue.edu /Ando-Basterra/abwgeec.txt (4612 words)

	Seminar BIU
		Give an example of a presheaf that is not a sheaf.
		(Introduce the notion of a sheaf associated to a preshaef.) Discuss when a sequence of sheaves is exact.
		Define the notion of an invertible sheaf and the Picard group.
	www.math.uni-bonn.de /people/bernd/SemBIU.html (760 words)

	Amazon.com: Books: Algebraic Varieties (London Mathematical Society Lecture Note Series) (Site not responding. Last check: 2007-09-16)
		An introduction to the theory of algebraic functions on varieties from a sheaf theoretic standpoint.
		For instance, an affine variety is defined as a space Y with a sheaf of k-algebras such that Mor(X,Y) is in natural bijection with k-Alg-Hom(k[Y],k[X]) for all other such spaces X which have a sheaf of k-algebras.
		It's slightly dense but the assiduous reader is rewarded heavily by an exposition which proves the Riemann-Roch theorem and covers sheaf cohomology in a relatively small exposition.
	www.amazon.com /exec/obidos/tg/detail/-/0521426138?v=glance (1120 words)

	[No title]
		The functions must be "compatible in this sense: on the intersection of two sets in the cover, the quotient of the corresponding rational functions should be regular and invertible.
		To every Cartier divisor D there is an associated line bundle (strictly, invertible sheaf) denoted by L[D], and the sum of divisors corresponds to the tensor product of line bundles.
		Isomorphism of bundles corresponds precisely to linear equivalence of Cartier divisors, and so the divisor classes give rise to the Picard group.
	50skills.co.za /infopages/index.php?title=Divisor_(algebraic_geometry) (399 words)

	A Note On A Question Of Fujita And A Conjecture Of Xiao (ResearchIndex) (Site not responding. Last check: 2007-09-16)
		Abstract: Introduction Let Y be a smooth variety of dimension m and M = O y (D) an invertible sheaf.
		If F is a locally free sheaf on Y we say that F is nef, strictly wf, ample or semiample if OP (1) is, where P = P Y (F).
		3 The sheaf of relative canonical forms of a Kahler fiber spac..
	citeseer.ist.psu.edu /190511.html (414 words)

	Math-Angers : Prépublication 177 (Site not responding. Last check: 2007-09-16)
		In this note, we study effective Cartier divisors with totally real or totally complex supports on a projective real curve.
		We give some numerical conditions for an invertible sheaf to be isomorphic or not to such a divisor.
		We show that these conditions are strongly related to the singularities of the curve and to topological properties of the real part of the Jacobian variety.
	math.univ-angers.fr /preprint/177.html (82 words)

	UIUC Mathematics Weekly Calendar
		The equivariant elliptic Thom sheaf of an equivariant spin bundle
		Abstract: Let V be a circle-equivariant spin bundle over a manifold M with circle action.
		The (equivariant) elliptic cohomology of V is an invertible sheaf over the elliptic cohomology of M. We show that this sheaf is universally the sheaf O(1) over a weighted projective space first considered by Looijenga.
	www.math.uiuc.edu /Bulletin/February/feb19-01wkly.html (944 words)

	Untitled Document (Site not responding. Last check: 2007-09-16)
		There exist sextics with an even set of 56 nodes.
		1) T can be viewed as a 3x3 matrix of linear forms on P3, thus determining an invertible sheaf G on a cubic surface G yielding a birational isomorphism with the plane
		4) In turn, E can be explicitly obtained as the extension of a trivial bundle of rank 6 through the sheaf G2(-1).
	www.mat.uniroma1.it /seminari/algebra-geometria/moduli/Catanese.html (179 words)

	Citations: Etale Cohomology - Milne (ResearchIndex) (Site not responding. Last check: 2007-09-16)
		In fact, if N is invertible in K, then we shall see later (cf.
		Viewing E[N ] as a (locally constant) etale sheaf of Z=NZ modules on S et, let 2 A E[N ] be its second exterior power with respect to A = Z=NZ (which is formed analogous to the tensor product of etale sheaves; cf.
		Corollary 2.2 Assume that n is invertible on X, then P ic(X; Y) nP ic(X; Y) ae H 2 et (X; j (n) here j is the extension by zero functor see [15] Proof: This follows from the lemma 2.1 in view of the exact sequence of etale sheaves: 0 Gamma j (n....
	citeseer.ist.psu.edu /context/15801/0 (2180 words)

	Zamora: Sheaves associated to holomorphic first integrals
		is rational we prove that the direct image sheaves of the co-normal sheaf of
		are locally free; and give some information on the nature of their decomposition as direct sum of invertible sheaves.
		VAN DE VEN, Compact Complex Surfaces, Springer Verlag,
	www.numdam.org /numdam-bin/item?id=AIF_2000__50_3_909_0 (142 words)

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