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231
On the geometry of DeligneMumford stacks
, 2006
"... Abstract. General structure results about Deligne–Mumford stacks are summarized, applicable to stacks of finite type over a field. When the base field has characteristic 0, a class of “(quasi)projective ” Deligne–Mumford stacks is identified, defined to be those that embed as a (locally) closed s ..."
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Cited by 6 (0 self)
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Abstract. General structure results about Deligne–Mumford stacks are summarized, applicable to stacks of finite type over a field. When the base field has characteristic 0, a class of “(quasi)projective ” Deligne–Mumford stacks is identified, defined to be those that embed as a (locally) closed
On motives for DeligneMumford stacks
, 2008
"... We define and compare two different definitions of Chow motives for DeligneMumford stacks, associated with two different definitions of Chow rings. The main result we prove is that both categories of motives are equivalent to the usual category of motives of algebraic varieties, but the motives of ..."
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Cited by 2 (0 self)
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We define and compare two different definitions of Chow motives for DeligneMumford stacks, associated with two different definitions of Chow rings. The main result we prove is that both categories of motives are equivalent to the usual category of motives of algebraic varieties, but the motives
Motivic integration over DeligneMumford stacks
, 2004
"... The aim of this article is to develop the theory of motivic integration over DeligneMumford stacks and to apply it to the birational geometry of DeligneMumford stacks. ..."
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Cited by 18 (4 self)
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The aim of this article is to develop the theory of motivic integration over DeligneMumford stacks and to apply it to the birational geometry of DeligneMumford stacks.
GROTHENDIECK DUALITY FOR DeligneMumford Stacks
, 2009
"... We prove the existence of the dualizing functor for a separated morphism of algebraic stacks with affine diagonal; then we explicitly develop duality for compact DeligneMumford stacks focusing in particular on the morphism from a stack to its coarse moduli space and on representable morphisms. We ..."
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Cited by 9 (0 self)
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We prove the existence of the dualizing functor for a separated morphism of algebraic stacks with affine diagonal; then we explicitly develop duality for compact DeligneMumford stacks focusing in particular on the morphism from a stack to its coarse moduli space and on representable morphisms
Quot functors for DeligneMumford stacks
 Comm. Algebra
"... Abstract. Given a separated and locally finitelypresented DeligneMumford stack X over an algebraic space S, and a locally finitelypresented OXmodule F, we prove that the Quot functor Quot(F/X/S) is represented by a separated and locally finitelypresented algebraic space over S. Under additional ..."
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Cited by 42 (5 self)
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Abstract. Given a separated and locally finitelypresented DeligneMumford stack X over an algebraic space S, and a locally finitelypresented OXmodule F, we prove that the Quot functor Quot(F/X/S) is represented by a separated and locally finitelypresented algebraic space over S. Under additional
SMOOTH TORIC DELIGNEMUMFORD STACKS
, 2009
"... We give a geometric definition of smooth toric DeligneMumford stacks using the action of a “torus”. We show that our definition is equivalent to the one of Borisov, Chen and Smith in terms of stacky fans. In particular, we give a geometric interpretation of the combinatorial data contained in a sta ..."
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Cited by 27 (0 self)
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We give a geometric definition of smooth toric DeligneMumford stacks using the action of a “torus”. We show that our definition is equivalent to the one of Borisov, Chen and Smith in terms of stacky fans. In particular, we give a geometric interpretation of the combinatorial data contained in a
On covering of DeligneMumford stacks and surjectivity of the Brauer map
 Bull. London Math. Soc
"... This paper is concerned with finite covers of Deligne–Mumford stacks by schemes, in connection with the theory of Brauer group. The reader is referred to [6] for basic references on algebraic stacks and Brauer groups. We are primarily concerned with Deligne–Mumford stacks; every ..."
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Cited by 28 (1 self)
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This paper is concerned with finite covers of Deligne–Mumford stacks by schemes, in connection with the theory of Brauer group. The reader is referred to [6] for basic references on algebraic stacks and Brauer groups. We are primarily concerned with Deligne–Mumford stacks; every
THE AUTOMORPHISM GROUP OF TORIC DeligneMumford Stacks
, 2007
"... We prove that the automorphism group of a toric DeligneMumford stack is isomorphic to the 2group associated to the stacky fan. ..."
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We prove that the automorphism group of a toric DeligneMumford stack is isomorphic to the 2group associated to the stacky fan.
On the conjecture of King for smooth toric DeligneMumford stacks
, 2008
"... Abstract. We construct full strong exceptional collections of line bundles on smooth toric Fano DeligneMumford stacks of Picard number at most two and of any Picard number in dimension two. It is hoped that the approach of this paper will eventually lead to the proof of the existence of such collec ..."
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Cited by 22 (0 self)
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Abstract. We construct full strong exceptional collections of line bundles on smooth toric Fano DeligneMumford stacks of Picard number at most two and of any Picard number in dimension two. It is hoped that the approach of this paper will eventually lead to the proof of the existence
Cone Theorem via DeligneMumford stacks
, 2005
"... We prove the cone theorem for varieties with LCIQ singularities using deformation theory of stable maps into DeligneMumford stacks. We also obtain a sharper bound on −(KX + D)degree of (KX +D)negative extremal rays for projective Qfactorial log terminal threefold pair (X, D). ..."
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Cited by 5 (5 self)
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We prove the cone theorem for varieties with LCIQ singularities using deformation theory of stable maps into DeligneMumford stacks. We also obtain a sharper bound on −(KX + D)degree of (KX +D)negative extremal rays for projective Qfactorial log terminal threefold pair (X, D).
Results 1  10
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231