Welschinger invariants of toric Del Pezzo surfaces with nonstandard real structures

E. Shustin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The Welschinger invariants of real rational algebraic surfaces are natural analogs of the Gromov-Witten invariants, and they estimate from below the number of real rational curves passing through prescribed configurations of points. We establish a tropical formula for the Welschinger invariants of four toric Del Pezzo surfaces equipped with a nonstandard real structure. Such a formula for real toric Del Pezzo surfaces with a standard real structure (i.e., naturally compatible with the toric structure) was established by Mikhalkin and the author. As a consequence we prove that for any real ample divisor D on a surface ∑ under consideration, through any generic configuration of c 1(∑)D - 1 generic real points, there passes a real rational curve belonging to the linear system |D|.

Original languageEnglish
Pages (from-to)218-246
Number of pages29
JournalProceedings of the Steklov Institute of Mathematics
Volume258
Issue number1
DOIs
StatePublished - Sep 2007

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