Equivariant Gromov–Witten invariants of algebraic GKM manifolds

Chiu Chu Melissa Liu, Artan Sheshmani

Research output: Contribution to journalArticlepeer-review


An algebraic GKM manifold is a non-singular algebraic variety equipped with an algebraic action of an algebraic torus, with only finitely many torus fixed points and finitely many 1-dimensional orbits. In this expository article, we use virtual localization to express equivariant Gromov–Witten invariants of any algebraic GKM manifold (which is not necessarily compact) in terms of Hodge integrals over moduli stacks of stable curves and the GKM graph of the GKM manifold.

Original languageEnglish (US)
Article number048
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
StatePublished - Jul 1 2017
Externally publishedYes


  • Equivariant cohomology
  • GKM manifold
  • Gromov
  • Localization
  • Moduli space
  • Witten theory

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Geometry and Topology


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