Fixed-point Localization for \mathbbRP^2m ⊂ \mathbbCP^2m

2017/03/08 by Amitai Netser Zernik, Zernik, Amitai Netser
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1703.02950

openalex publication_date 2017/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive a fixed-point formula for integrals on moduli spaces of stable maps to projective spaces of even dimension. This gives a formula for the equivariant open Gromov-Witten invariants of (RP^2m,CP^2m) and the structure constants of the equivariant Fukaya A-infinity algebra of RP²m in CP^2m with bulk deformations. The formula involves contributions from Givental's correlators for the closed theory and the descendent integrals of discs, and specializes to give a new expression for the Welschinger count of real rational curves in the plane passing through some real and conjugation invariant pairs of points.

Citations

• The open Gromov-Witten-Welschinger theory of blowups of the projective plane
• Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions

Related

• Equivariant Open Gromov-Witten Theory of ℝℙ^2m \hookrightarrow ℂℙ^2m
• Integration on moduli spaces of stable curves through localization
• Moduli spaces of point configurations and plane curve counts
• A TQFT of Intersection Numbers on Moduli Spaces of Admissible Covers
• Invariants of stable quasimaps with fields