The invariance of higher genus Welschinger invariants of del Pezzo surfaces

A higher genus version of Welschinger invariant was defined by Shustin for del Pezzo surfaces. These invariants count real curves of positive genera with signs. We study the properties of higher genus Welschinger invariants under Morse simplification. When the signs are defined by the number of solitary nodes, we prove that these higher genus Welschinger invariants depend only on the total number of real interpolated points. The result follows from a reduction of the genus and Brugallé's result on the invariance of genus zero Welschinger invariants.