Relative enumerative invariants of real nodal del Pezzo surfaces

Abstract

The surfaces considered are real, rational and have a unique smooth real $$(-2)$$ -curve. Their canonical class K is strictly negative on any other irreducible curve in the surface and $$K^2>0$$ . For surfaces satisfying these assumptions, we suggest a certain signed count of real rational curves that belong to a given divisor class and are simply tangent to the $$(-2)$$ -curve at each intersection point. We prove that this count provides a number which depends neither on the point constraints nor on deformation of the surface preserving the real structure and the $$(-2)$$ -curve.