Relative enumerative invariants of real nodal del Pezzo surfaces

Ilia Itenberg; Viatcheslav Kharlamov; Eugenii Shustin

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arXiv · 1611.02938

Relative enumerative invariants of real nodal del Pezzo surfaces

Ilia Itenberg·Viatcheslav Kharlamov·Eugenii Shustin

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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.

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BibTeX RIS

Ilia Itenberg, Viatcheslav Kharlamov, Eugenii Shustin. 2018-05-15. Relative enumerative invariants of real nodal del Pezzo surfaces. https://arxiv.org/abs/1611.02938

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