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Deformation theory of objects in homotopy and derived categories I: General theory
, 2008
"... This is the first paper in a series. We develop a general deformation theory of objects in homotopy and derived categories of DG categories. Namely, for a DG module E over a DG category we define four deformation functors Def h (E) , coDef h (E) , Def(E) , coDef(E). The first two functors describe ..."
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Cited by 5 (4 self)
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This is the first paper in a series. We develop a general deformation theory of objects in homotopy and derived categories of DG categories. Namely, for a DG module E over a DG category we define four deformation functors Def h (E) , coDef h (E) , Def(E) , coDef(E). The first two functors describe the deformations (and codeformations) of E in the homotopy
doi:10.1093/imrn/rnp050 On Hochschild Cohomology and Morita Deformations
, 2009
"... In this paper we show that, in general, firstorder Morita deformations are too limited ..."
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In this paper we show that, in general, firstorder Morita deformations are too limited
unknown title
"... The following thesis plays a central role in deformation theory: (∗) If X is a moduli space over a field k of characteristic zero, then a formal neighborhood of any point x ∈ X is controlled by a differential graded Lie algebra. This idea was developed in unpublished work of Deligne, Drinfeld, and F ..."
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The following thesis plays a central role in deformation theory: (∗) If X is a moduli space over a field k of characteristic zero, then a formal neighborhood of any point x ∈ X is controlled by a differential graded Lie algebra. This idea was developed in unpublished work of Deligne, Drinfeld, and Feigin, and has powerfully influenced
Hochschild homology and Gabber’s Theorem
, 2006
"... About twentyfive O. Gabber proved his famous theorem [G] which claims, roughly speaking, that the singular support SS(F) of a Dmodule F on a smooth algebraic manifold M is an involutive subvariety in the cotangent ..."
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About twentyfive O. Gabber proved his famous theorem [G] which claims, roughly speaking, that the singular support SS(F) of a Dmodule F on a smooth algebraic manifold M is an involutive subvariety in the cotangent
ON INCIDENCE BETWEEN STRATA OF THE HILBERT SCHEME OF POINTS ON P 2
, 2005
"... Abstract. The Hilbert scheme of n points in the projective plane has a natural stratification obtained from the associated Hilbert series. In general, the precise inclusion relation between the closures of the strata is still unknown. In [11] Guerimand studied this problem for strata whose Hilbert s ..."
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Abstract. The Hilbert scheme of n points in the projective plane has a natural stratification obtained from the associated Hilbert series. In general, the precise inclusion relation between the closures of the strata is still unknown. In [11] Guerimand studied this problem for strata whose Hilbert series are as close as possible. Preimposing a certain technical condition he obtained necessary and sufficient conditions for the incidence of such strata. In this paper we present a new approach, based on deformation theory, to Guerimand’s result. This allows us to show that the technical condition is not necessary.
DG DEFORMATION THEORY OF OBJECTS IN HOMOTOPY AND DERIVED CATEGORIES I
, 2006
"... Abstract. We develop a general deformation theory of objects in homotopy and derived categories of DG categories. The main result is a general prorepresentability theorem for the corresponding deformation functor. ..."
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Abstract. We develop a general deformation theory of objects in homotopy and derived categories of DG categories. The main result is a general prorepresentability theorem for the corresponding deformation functor.
Contents
, 2007
"... Abstract. This is the third paper in a series. In part I we developed a deformation theory of objects in homotopy and derived categories of DG categories. Here we show how this theory can be used to study deformations of objects in homotopy and derived categories of abelian categories. Then we consi ..."
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Abstract. This is the third paper in a series. In part I we developed a deformation theory of objects in homotopy and derived categories of DG categories. Here we show how this theory can be used to study deformations of objects in homotopy and derived categories of abelian categories. Then we consider examples from algebraic geometry.
ON THE DEFORMATION THEORY OF PAIR (X, E)
, 809
"... Abstract. Huybrechts and Thomas recently constructed relative obstruction theory of objects of the derived category of coherent sheaves over smooth projective family. In this paper, we use this construction to obtain the absolute deformationobstruction theory of the pair (X, E), with X smooth proje ..."
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Abstract. Huybrechts and Thomas recently constructed relative obstruction theory of objects of the derived category of coherent sheaves over smooth projective family. In this paper, we use this construction to obtain the absolute deformationobstruction theory of the pair (X, E), with X smooth projective scheme and E perfect complex, and show that the obstruction theories for E,(X, E), and X fit into exact triangle as derived objects on the moduli space. 1.