Higher genus Welschinger invariants under real surgeries

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.

16 pages. The main theorem is restricted to the real del Pezzo surfaces, and the formula is also considered in the symplectic case in the Appendix

References in corpus (2)

• On higher genus Welschinger invariants of Del Pezzo surfaces
• Welschinger invariants of Blow-ups of symplectic 4-manifolds