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

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.

23 pages, we corrected a few minor misprints, clarified the proof of Theorem 1.1.2, corrected Table 6 and the claim of Theorem 5.1.1

References in corpus (1)

• Welschinger invariants of real del Pezzo surfaces of degree $\ge 2$