Results 1  10
of
11,798
On Quantum Cohomology
, 1996
"... Abstract We discuss a general quantum theoretical example of quantum cohomology and show that various mathematical aspects of quantum cohomology have quantum mechanical and also observable significance. 1 The quantum cohomology is one of the most fundamental and intressting mathematicalphysical fie ..."
Abstract
 Add to MetaCart
Abstract We discuss a general quantum theoretical example of quantum cohomology and show that various mathematical aspects of quantum cohomology have quantum mechanical and also observable significance. 1 The quantum cohomology is one of the most fundamental and intressting mathematical
GromovWitten classes, quantum cohomology, and enumerative geometry
 Commun. Math. Phys
, 1994
"... The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov–Witten classes, and a discussion of their properties for Fano varieties. Cohomological ..."
Abstract

Cited by 474 (3 self)
 Add to MetaCart
The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov–Witten classes, and a discussion of their properties for Fano varieties. Cohomological
Quantum cohomology of complete intersections
, 1995
"... The quantum cohomology algebra of a projective manifold X is the cohomology of X endowed with a different algebra structure, which takes into account the geometry of rational curves in X. This structure has been first defined heuristically ..."
Abstract

Cited by 41 (0 self)
 Add to MetaCart
The quantum cohomology algebra of a projective manifold X is the cohomology of X endowed with a different algebra structure, which takes into account the geometry of rational curves in X. This structure has been first defined heuristically
Quantum Cohomology Of Flag Varieties
 Internat. Math. Res. Notices
, 1995
"... Introduction The quantum cohomology ring of a Kahler manifold X is a deformation of the usual cohomology ring which appears naturally in theoretical physics in the study of the supersymmetric nonlinear sigma models with target X. In [W], Witten introduces the quantum multiplication of cohomology cl ..."
Abstract

Cited by 41 (2 self)
 Add to MetaCart
Introduction The quantum cohomology ring of a Kahler manifold X is a deformation of the usual cohomology ring which appears naturally in theoretical physics in the study of the supersymmetric nonlinear sigma models with target X. In [W], Witten introduces the quantum multiplication of cohomology
Quantum cohomology rings of toric manifolds
, 1993
"... We compute the quantum cohomology ring H ∗ ϕ(PΣ,C) of an arbitrary ddimensional smooth projective toric manifold PΣ associated with a fan Σ. The multiplicative structure of H ∗ ϕ (PΣ,C) depends on the choice of an element ϕ in the ordinary cohomology group H 2 (PΣ,C). There are many properties of q ..."
Abstract

Cited by 95 (2 self)
 Add to MetaCart
We compute the quantum cohomology ring H ∗ ϕ(PΣ,C) of an arbitrary ddimensional smooth projective toric manifold PΣ associated with a fan Σ. The multiplicative structure of H ∗ ϕ (PΣ,C) depends on the choice of an element ϕ in the ordinary cohomology group H 2 (PΣ,C). There are many properties
Quantum cohomology of Grassmannians
 Compositio Math
"... The purpose of this paper is to give simple proofs of the main theorems about quantum cohomology of Grassmannians. This first of all includes Bertram’s quantum versions of the Pieri and Giambelli formulas [1]. Bertram’s proofs of these theorems required the use of quot schemes. Our proof of the quan ..."
Abstract

Cited by 34 (6 self)
 Add to MetaCart
The purpose of this paper is to give simple proofs of the main theorems about quantum cohomology of Grassmannians. This first of all includes Bertram’s quantum versions of the Pieri and Giambelli formulas [1]. Bertram’s proofs of these theorems required the use of quot schemes. Our proof
The quantum cohomology of homogeneous varieties
 J. Algebraic Geom
, 1997
"... The notion of quantum cohomology was first proposed by Witten [Va, Wi], based on topological field theory. Its mathematical theory was only established recently by Y. Ruan and the second named author [RT, Ru], where they proved the existence of the quantum rings on semipositive symplectic manifolds ..."
Abstract

Cited by 20 (1 self)
 Add to MetaCart
The notion of quantum cohomology was first proposed by Witten [Va, Wi], based on topological field theory. Its mathematical theory was only established recently by Y. Ruan and the second named author [RT, Ru], where they proved the existence of the quantum rings on semipositive symplectic
On the quantum cohomology of adjoint varieties
 Proc. of the London Math. Soc., arχiv:0904:4824v1
"... We study the quantum cohomology of quasiminuscule and quasicominuscule homogeneous spaces. The product of any two Schubert cells does not involve powers of the quantum parameter higher than 2. With the help of the quantum to classical principle we give presentations of the quantum cohomology algeb ..."
Abstract

Cited by 9 (3 self)
 Add to MetaCart
We study the quantum cohomology of quasiminuscule and quasicominuscule homogeneous spaces. The product of any two Schubert cells does not involve powers of the quantum parameter higher than 2. With the help of the quantum to classical principle we give presentations of the quantum cohomology
Quantum cohomology of flag manifolds
"... In this paper, we study the (small) quantum cohomology ring of the partial flag manifold. We give proofs of the presentation of the ring and of the quantum Giambelli formula for Schubert varieties. These are known results, but our proofs are more natural and direct than the previous ones. ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
In this paper, we study the (small) quantum cohomology ring of the partial flag manifold. We give proofs of the presentation of the ring and of the quantum Giambelli formula for Schubert varieties. These are known results, but our proofs are more natural and direct than the previous ones.
Orbifold Quantum Cohomology
, 2000
"... This is a research announcement on a theory of GromovWitten invariants and quantum cohomology of symplectic or projective orbifolds. Our project started in the summer of 98 where our original motivation was to study the quantum cohomology under singular flops in complex dimension three. In this set ..."
Abstract

Cited by 10 (0 self)
 Add to MetaCart
This is a research announcement on a theory of GromovWitten invariants and quantum cohomology of symplectic or projective orbifolds. Our project started in the summer of 98 where our original motivation was to study the quantum cohomology under singular flops in complex dimension three
Results 1  10
of
11,798