Higher genus Welschinger invariants under real surgeries

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.