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512
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 386 (34 self)
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We prove that the canonical ring of a smooth projective variety is finitely generated.
Virtual moduli cycles and Gromov-Witten 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
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 336 (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 n-pointed Riemann surfaces of genus g. Denote by M n g the Deligne-Mumford 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 207 (2 self)
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Let M n g be the moduli space of n-pointed Riemann surfaces of genus g. Denote by M n g the Deligne-Mumford 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 well-known 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 well-known 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 143 (9 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
Notes On Stable Maps And Quantum Cohomology
, 1996
"... Contents 0. Introduction 1 1. Stable maps and their moduli spaces 10 2. Boundedness and a quotient approach 12 5. The construction of M g;n (X; fi) 25 6. The boundary of M 0;n (X; fi) 29 7. Gromov-Witten invariants 31 8. Quantum cohomology 34 9. Applications to enumerative geometry 38 10. Varia ..."
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Cited by 141 (14 self)
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Contents 0. Introduction 1 1. Stable maps and their moduli spaces 10 2. Boundedness and a quotient approach 12 5. The construction of M g;n (X; fi) 25 6. The boundary of M 0;n (X; fi) 29 7. Gromov-Witten invariants 31 8. Quantum cohomology 34 9. Applications to enumerative geometry 38 10. Variations 43 References 46 0. Introduction 0.1. Overview. The aim of these notes is to describe an exciting chapter in the recent development of quantum cohomology. Guided by ideas from physics (see [W]), a remarkable structure on the solutions of certain rational enumerative geometry problems has been found: the solutions are coefficients in the multiplication table of a quantum cohomology ring. Associativity of the ring yields non-trivial relations among the enumerative solutions. In many cases, these relations suffice to solve the enumerative problem. For example, let N d be the number of degree d, rational plane curves passing through 3d \Gamma 1 general points in P . Since there is a un
