On wall-crossing invariance of certain sums of Welschinger numbers

Abstract

We continue our quest for real enumerative invariants not sensitive to changing the real structure and extend the construction we uncovered previously for counting curves of anti-canonical degree $$\leqslant 2$$ on del Pezzo surfaces with $$K^2=1$$ to curves of any anti-canonical degree and on any del Pezzo surfaces of degree $$K^2\leqslant 3$$ .