The open Gromov-Witten-Welschinger theory of blowups of the projective plane

TL;DR

This paper develops a recursive method to compute Welschinger invariants for blowups of the projective plane, extending open Gromov-Witten theory and providing explicit calculations even in non-del Pezzo cases.

Contribution

It introduces an open Gromov-Witten-Welschinger framework for blowups of the projective plane and derives recursive formulas based on open analogues of classical axioms.

Findings

Recursive algorithm for invariants reconstruction

Explicit computations for non-del Pezzo cases

Extension of open Gromov-Witten theory to blowups

Abstract

We compute the Welschinger invariants of blowups of the projective plane at an arbitrary conjugation invariant configuration of points. Specifically, open analogues of the WDVV equation and Kontsevich-Manin axioms lead to a recursive algorithm that reconstructs all the invariants from a small set of known invariants. Example computations are given, including the non-del Pezzo case.