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503
Existence of minimal models for varieties of log general type
 J. AMER. MATH. SOC
, 2008
"... We prove that the canonical ring of a smooth projective variety is finitely generated. ..."
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Cited by 381 (37 self)
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We prove that the canonical ring of a smooth projective variety is finitely generated.
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. ..."
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Cited by 347 (9 self)
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We suggest a construction of virtual fundamental classes of certain types of moduli spaces.
Towards an enumerative geometry of the moduli space of curves
 in Arithmetic and Geometry
, 1983
"... The goal of this paper is to formulate and to begin an exploration of the enumerative geometry of the set of all curves of arbitrary genus g. By this we mean setting up a Chow ring for the moduli space M g of curves of genus g and its compactification.M 9, defining what seem to be ..."
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Cited by 331 (0 self)
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The goal of this paper is to formulate and to begin an exploration of the enumerative geometry of the set of all curves of arbitrary genus g. By this we mean setting up a Chow ring for the moduli space M g of curves of genus g and its compactification.M 9, defining what seem to be
Euler characteristics of moduli spaces of curves
, 2008
"... Let M n g be the moduli space of npointed Riemann surfaces of genus g. Denote by M n g the DeligneMumford compactification of M n g. In the present paper, we calculate the orbifold and the ordinary Euler characteristic of M n g for any g and n such that n> 2 − 2g. ..."
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Cited by 201 (2 self)
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Let M n g be the moduli space of npointed Riemann surfaces of genus g. Denote by M n g the DeligneMumford compactification of M n g. In the present paper, we calculate the orbifold and the ordinary Euler characteristic of M n g for any g and n such that n> 2 − 2g.
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 183 (23 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
Conformal blocks and generalized theta functions
 Comm. Math. Phys
, 1994
"... The aim of this paper is to construct a canonical isomorphism between two vector spaces associated to a Riemann surface X. The first of these spaces is the space of conformal blocks Bc(r) (also called the space of vacua), which plays an important role in conformal field theory. It is defined as foll ..."
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Cited by 141 (8 self)
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The aim of this paper is to construct a canonical isomorphism between two vector spaces associated to a Riemann surface X. The first of these spaces is the space of conformal blocks Bc(r) (also called the space of vacua), which plays an important role in conformal field theory. It is defined as follows: choose a point p ∈ X, and let AX be the