Relative enumerative invariants of real nodal del Pezzo surfaces

Ilia Itenberg, Viatcheslav Kharlamov, Eugenii Shustin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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 K2> 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.

Original languageEnglish
Pages (from-to)2927-2990
Number of pages64
JournalSelecta Mathematica, New Series
Volume24
Issue number4
DOIs
StatePublished - 1 Sep 2018

Funding

FundersFunder number
Hermann-Minkowski-Minerva Center for Geometry
Israeli Science Foundation448/09, 176/15
German-Israeli Foundation for Scientific Research and Development1174-197.6/2011
Tel Aviv University

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