Combined count of real rational curves of canonical degree 2 on real del Pezzo surfaces with K²=1

2021/07/14 by Finashin, Sergey, Kharlamov, Viatcheslav
#14J26 #14N15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary: 14N10. Secondary: 14P25

paper · doi:10.48550/arxiv.2107.06988

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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