Quantum Kirwan morphism and Gromov-Witten invariants of quotients I

Chris T. Woodward

Quantum Kirwan morphism and Gromov-Witten invariants of quotients I

Algebraic Geometry 2017-05-19 v9 Symplectic Geometry

Authors: Chris T. Woodward

Abstract

This is the first in a sequence of papers in which we construct a quantum version of the Kirwan map from the equivariant quantum cohomology $QH_G(X)$ of a smooth complex projective variety X with the action of a connected complex reductive group $G$ to the orbifold quantum cohomology $QH(X//G)$ of its geometric invariant theory quotient $X//G$ , and prove that it intertwines the genus zero gauged Gromov-Witten potential of X with the genus zero Gromov-Witten graph potential of $X//G$ .

Keywords

quantum Kirwan morphism Gromov-Witten invariants equivariant quantum cohomology geometric invariant theory quotient gauged Gromov-Witten potential

Cite

@article{arxiv.1204.1765,
  title  = {Quantum Kirwan morphism and Gromov-Witten invariants of quotients I},
  author = {Chris T. Woodward},
  journal= {arXiv preprint arXiv:1204.1765},
  year   = {2017}
}

Comments

51 pages, 11 figures. Appeared in Transform. Groups. In this version a missing cotangent line on page 31 of part II is fixed, with a consequent change in a few other formulas

Quantum Kirwan morphism and Gromov-Witten invariants of quotients I

Abstract

Keywords

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