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157
CHERN CLASSES IN DELIGNE COHOMOLOGY FOR COHERENT ANALYTIC SHEAVES
, 712
"... Abstract. In this article, we construct Chern classes in rational Deligne cohomology for coherent sheaves on a smooth compact complex manifold. We prove that these classes satisfy the functoriality property under pullbacks, the Whitney formula and the GrothendieckRiemannRoch theorem for an immersi ..."
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for an immersion. This answers the question of proving that if F is a coherent sheaf of rank i on X, the topological Chern class ci(F) top ofF in H 2i (X, Q) lies in F i H 2i (X, C). Contents
Singular support of coherent sheaves, and the geometric Langlands conjecture
"... Abstract. We define the notion of singular support of a coherent sheaf on a quasismooth derived (DG) scheme or Artin stack, where “quasismooth ” means that it is a locally complete intersection in the derived sense. This develops the idea of “cohomological ” support of coherent sheaves on a locall ..."
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Cited by 26 (11 self)
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Abstract. We define the notion of singular support of a coherent sheaf on a quasismooth derived (DG) scheme or Artin stack, where “quasismooth ” means that it is a locally complete intersection in the derived sense. This develops the idea of “cohomological ” support of coherent sheaves on a
Cohomology of coherent sheaves on a proper scheme
, 1992
"... Let f: X → S be a proper morphism where S = Spec A where A is a noetherian ring. Let F be a coherent sheaf on X. Then a theorem of Grothendieck says that the cohomology groups H i (X, F) are Amodules of finite type. We set out to give an algorithm to compute these Amodules when A is sufficiently a ..."
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Let f: X → S be a proper morphism where S = Spec A where A is a noetherian ring. Let F be a coherent sheaf on X. Then a theorem of Grothendieck says that the cohomology groups H i (X, F) are Amodules of finite type. We set out to give an algorithm to compute these Amodules when A is sufficiently
Moduli schemes of rank one Azumaya modules
"... Let X be a smooth projective variety, e. g. a surface, over an algebraically closed field k. Let A be a torsion free coherent sheaf of algebras over X, e.g. a sheaf of Azumaya algebras; we always assume that the generic fiber Aη is a ..."
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Let X be a smooth projective variety, e. g. a surface, over an algebraically closed field k. Let A be a torsion free coherent sheaf of algebras over X, e.g. a sheaf of Azumaya algebras; we always assume that the generic fiber Aη is a
THE HORROCKS CORRESPONDENCE FOR COHERENT SHEAVES ON PROJECTIVE SPACES
, 2008
"... We establish an equivalence between the stable category of coherent sheaves (satisfying a mild restriction) on a projective space and the homotopy category of a certain class of minimal complexes of free modules over the exterior algebra Koszul dual to the homogeneous coordinate algebra of the proje ..."
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of Horrocks [14], [15]. We also give direct proofs of the BGG correspondences for graded modules and for coherent sheaves and of the theorem of Eisenbud, Fløystad and Schreyer [11] describing the linear part of the Tate resolution associated to a coherent sheaf. Moreover, we provide an explicit description
The Beilinson complex and canonical rings of irregular surfaces
, 2006
"... An important theorem by Beilinson describes the bounded derived category of coherent sheaves on Pn, yielding in particular a resolution of every coherent sheaf on Pn in terms of the vector bundles Ω j Pn(j) for 0 ≤ j ≤ n. This theorem is here extended to weighted projective spaces. To this purpose ..."
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Cited by 10 (1 self)
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An important theorem by Beilinson describes the bounded derived category of coherent sheaves on Pn, yielding in particular a resolution of every coherent sheaf on Pn in terms of the vector bundles Ω j Pn(j) for 0 ≤ j ≤ n. This theorem is here extended to weighted projective spaces. To this purpose
TATE RESOLUTIONS AND WEYMAN COMPLEXES
, 2009
"... We construct generalized Weyman complexes for coherent sheaves on projective space and describe explicitly how the differential depend on the differentials in the correpsonding Tate resolution. We apply this to define the Weyman complex of a coherent sheaf on a projective variety and explain how ce ..."
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We construct generalized Weyman complexes for coherent sheaves on projective space and describe explicitly how the differential depend on the differentials in the correpsonding Tate resolution. We apply this to define the Weyman complex of a coherent sheaf on a projective variety and explain how
CONNECTIONS FOR WEIGHTED PROJECTIVE LINES
, 904
"... Abstract. We introduce a notion of a connection on a coherent sheaf on a weighted projective line (in the sense of Geigle and Lenzing). Using a theorem of Hübner and Lenzing we show, under a mild hypothesis, that if one considers coherent sheaves equipped with such a connection, and one passes to ..."
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Abstract. We introduce a notion of a connection on a coherent sheaf on a weighted projective line (in the sense of Geigle and Lenzing). Using a theorem of Hübner and Lenzing we show, under a mild hypothesis, that if one considers coherent sheaves equipped with such a connection, and one passes to
A.: Master spaces for stable pairs
 Topology
, 1998
"... In this paper we construct master spaces for certain coupled vector bundle problems over a fixed projective variety X. From a technical point of view, master spaces classify oriented pairs (E, ε, ϕ) consisting of a torsion free coherent sheaf E with fixed Hilbert polynomial, an ..."
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Cited by 9 (2 self)
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In this paper we construct master spaces for certain coupled vector bundle problems over a fixed projective variety X. From a technical point of view, master spaces classify oriented pairs (E, ε, ϕ) consisting of a torsion free coherent sheaf E with fixed Hilbert polynomial, an
The resolution property for schemes and stacks
"... Abstract. We prove the equivalence of two fundamental properties of algebraic stacks: being a quotient stack in a strong sense, and the resolution property, which says that every coherent sheaf is a quotient of some vector bundle. Moreover, we prove these properties in the important special case of ..."
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Abstract. We prove the equivalence of two fundamental properties of algebraic stacks: being a quotient stack in a strong sense, and the resolution property, which says that every coherent sheaf is a quotient of some vector bundle. Moreover, we prove these properties in the important special case
Results 11  20
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157