Relative enumerative invariants of real nodal del Pezzo surfaces

2016/11/09 by Itenberg, Ilia, Kharlamov, Viatcheslav, Shustin, Eugenii · 2 citations
#14J26 #14N10 #14P05 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1611.02938

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 K²>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.

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