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Compactifying the space of stable maps
 electronic), 2002. OLSSON AND STARR
"... Abstract. In this paper we study a notion of twisted stable map, from a curve to a tame Deligne–Mumford stack, which generalizes the wellknown notion of stable map to a projective variety. Contents ..."
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Cited by 186 (22 self)
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Abstract. In this paper we study a notion of twisted stable map, from a curve to a tame Deligne–Mumford stack, which generalizes the wellknown notion of stable map to a projective variety. Contents
Complete moduli in the presence of semiabelian group action
 Ann. of Math
"... Abstract. I prove the existence, and describe the structure, of moduli space of pairs (P, Θ) consisting of a projective variety P with semiabelian group action and an ample Cartier divisor on it satisfying a few simple conditions. Every connected component of this moduli space is proper. A component ..."
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Cited by 103 (7 self)
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Abstract. I prove the existence, and describe the structure, of moduli space of pairs (P, Θ) consisting of a projective variety P with semiabelian group action and an ample Cartier divisor on it satisfying a few simple conditions. Every connected component of this moduli space is proper. A component containing a projective toric variety is described by a configuration of several polytopes the main of which is the secondary polytope. On the other hand, the component containing a principally polarized abelian variety provides a moduli compactification of Ag. The main irreducible component of this compactification is described by an ”infinite periodic ” analog of secondary polytope and coincides with the
Homotopical algebraic geometry. II. Geometric stacks and applications
, 2006
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Derived Categories of Twisted Sheaves on CalabiYau Manifolds
, 2000
"... This dissertation is primarily concerned with the study of derived categories of twisted sheaves on CalabiYau manifolds. Twisted sheaves occur naturally in a variety of problems, but the most important situation where they are relevant is in the study of moduli problems of semistable sheaves on var ..."
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Cited by 88 (3 self)
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This dissertation is primarily concerned with the study of derived categories of twisted sheaves on CalabiYau manifolds. Twisted sheaves occur naturally in a variety of problems, but the most important situation where they are relevant is in the study of moduli problems of semistable sheaves on varieties. Although universal sheaves may not exist as such, in many cases one can construct them as twisted universal sheaves. In fact, the twisting is an intrinsic property of the moduli problem under consideration. A fundamental construction due to Mukai associates to a universal sheaf a transform between the derived category of the original space and the derived category of the moduli space, which often turns out to be an equivalence. In the present work we study what happens when the universal sheaf is replaced by a twisted one. Under these circumstances we obtain a transform between the de