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229
Virtual moduli cycles and GromovWitten invariants of algebraic varieties
, 1998
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The Intrinsic Normal Cone
 Invent. Math
, 1997
"... We suggest a construction of virtual fundamental classes of certain types of moduli spaces. Contents 0 ..."
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Cited by 353 (9 self)
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We suggest a construction of virtual fundamental classes of certain types of moduli spaces. Contents 0
Localization of virtual classes
"... We prove a localization formula for the virtual fundamental class in the general context of C∗equivariant perfect obstruction theories. Let X be an algebraic scheme with a C∗action and a C∗equivariant perfect obstruction theory. The virtual fundamental class [X] vir in ..."
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Cited by 260 (37 self)
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We prove a localization formula for the virtual fundamental class in the general context of C∗equivariant perfect obstruction theories. Let X be an algebraic scheme with a C∗action and a C∗equivariant perfect obstruction theory. The virtual fundamental class [X] vir in
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
Equivariant Intersection Theory
 Invent. Math
, 1996
"... this paper is to develop an equivariant intersection theory for actions of linear algebraic groups on algebraic schemes. The theory is based on our construction of equivariant Chow groups. They are algebraic analogues of equivariant cohomology groups which have all the functorial properties of ordin ..."
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Cited by 161 (18 self)
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this paper is to develop an equivariant intersection theory for actions of linear algebraic groups on algebraic schemes. The theory is based on our construction of equivariant Chow groups. They are algebraic analogues of equivariant cohomology groups which have all the functorial properties of ordinary Chow groups. In addition, they enjoy many of the properties of equivariant cohomology
The Orbifold Chow Ring of Toric DeligneMumford Stacks
 JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY
, 2004
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STABLE MORPHISMS TO SINGULAR SCHEMES AND RELATIVE STABLE MORPHISMS
"... Let W/C be a degeneration of smooth varieties so that the special fiber has normal crossing singularity. In this paper, we first construct the stack of expanded degenerations of W. We then construct the moduli space of stable morphisms to this stack, which provides a degeneration of the moduli spa ..."
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Cited by 101 (5 self)
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Let W/C be a degeneration of smooth varieties so that the special fiber has normal crossing singularity. In this paper, we first construct the stack of expanded degenerations of W. We then construct the moduli space of stable morphisms to this stack, which provides a degeneration of the moduli spaces of stable morphisms associated to W/C. Using a similar technique, for a pair (Z, D) of smooth variety and a smooth divisor, we construct the stack of expanded relative pairs and then the moduli spaces of relative stable morphisms to (Z, D). This is the algebrogeometric analogue of DonaldsonFloer theory in gauge theory. The construction of relative GromovWitten invariants and the degeneration formula of GromovWitten invariants will be treated in the subsequent paper.
Cycle groups for Artin stacks
 Invent. Math
, 1999
"... 2. Definition and basic properties 2 3. Elementary intersection theory 16 4. Extended excision axiom 22 ..."
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Cited by 94 (3 self)
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2. Definition and basic properties 2 3. Elementary intersection theory 16 4. Extended excision axiom 22
A DEGENERATION FORMULA OF GWINVARIANTS
, 2001
"... This is the sequel to the paper [Li]. In this paper, we construct the virtual moduli cycles of the degeneration of the moduli of stable morphisms constructed in [Li]. We also construct the virtual moduli cycles of the moduli of relative stable morphisms of a pair of a smooth divisor in a smooth var ..."
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Cited by 84 (4 self)
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This is the sequel to the paper [Li]. In this paper, we construct the virtual moduli cycles of the degeneration of the moduli of stable morphisms constructed in [Li]. We also construct the virtual moduli cycles of the moduli of relative stable morphisms of a pair of a smooth divisor in a smooth variety. Based on these, we prove a degeneration formula of the GromovWitten invariants.