COMBINED COUNT OF REAL RATIONAL CURVES OF CANONICAL DEGREE 2 ON REAL DEL PEZZO SURFACES WITH

We propose two systems of “intrinsic” weights 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...

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Bibliographic Details
Published in:Journal of the Institute of Mathematics of Jussieu 2024-01, Vol.23 (1), p.123-148
Main Authors: Finashin, S., Kharlamov, V.
Format: Article
Language:English
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Summary:We propose two systems of “intrinsic” weights 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.
ISSN:1474-7480
1475-3030
DOI:10.1017/S1474748022000317