Equivariant Open Gromov-Witten Theory of $\mathbb{R}{\mathbb{P}}^{2m}\hookrightarrow \mathbb{C}{\mathbb{P}}^{2m}$

Abstract

We define equivariant open Gromov-Witten invariants for $\mathbb{R}{\mathbb{P}}^{2m}\hookrightarrow \mathbb{C}{\mathbb{P}}^{2m}$ as sums of integrals of equivariant forms over resolution spaces, which are blowups of products of moduli spaces of stable disc-maps modeled on trees. These invariants encode the quantum deformation of the equivariant cohomology of $\mathbb{R}{\mathbb{P}}^{2m}$ by holomorphic discs in $\mathbb{C}{\mathbb{P}}^{2m}$ and, for $m=1$, specialize to give Welschinger's signed count of real rational planar curves in the non-equivariant limit.

arXiv admin note: text overlap with arXiv:1709.07402

References in corpus (2)

• Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions
• Moduli of Open Stable Maps to a Homogeneous Space