Higher genus Welschinger invariants under real surgeries

TL;DR

This paper investigates how higher genus Welschinger invariants change under real surgeries on real del Pezzo surfaces, providing a formula that relates invariants before and after surgery, advancing understanding in real enumerative geometry.

Contribution

It introduces a genus decreasing formula for Welschinger invariants under real surgeries, revealing their behavior in higher genus cases.

Findings

Derived a genus decreasing formula for Welschinger invariants

Analyzed the effect of real surgeries on invariants

Enhanced understanding of real enumerative geometry

Abstract

According to [3], a real surgery of a real del Pezzo surface $X_\mathbb{R}$ along a real sphere $S$ is a modification of the real structure on $X_\mathbb{R}$ in a neighborhood of $S$. In this paper, we study the behavior of higher genus Welschinger invariants under real surgeries, and obtain a genus decreasing formula of Welschinger invariants.