Fixed-point Localization for RP²ᵐ ⊂ CP²ᵐ

الأصل · EN

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 (RP²ᵐ,CP²ᵐ) and the structure constants of the equivariant Fukaya A-infinity algebra of RP²m in CP²ᵐ 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.