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arXiv · 2107.06988

Combined count of real rational curves of canonical degree 2 on real del Pezzo surfaces with $K^2=1$

Sergey Finashin·Viatcheslav Kharlamov
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Abstract

We propose two systems of "intrinsic" signs for counting such curves. In both cases the result acquires an exceptionally strong invariance property: it does not depend on the choice of a surface. One of our counts includes all divisor classes of canonical degree 2 and gives in total 30. The other one excludes the class $-2K$, but adds up the results of counting for a pair of real structures that differ by Bertini involution. This count gives 96.

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Sergey Finashin, Viatcheslav Kharlamov. 2021-07-14. Combined count of real rational curves of canonical degree 2 on real del Pezzo surfaces with $K^2=1$. https://arxiv.org/abs/2107.06988

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