Welschinger invariants of toric Del Pezzo surfaces with nonstandard real structures

E. Shustin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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
Issue number1
StatePublished - Sep 2007


FundersFunder number
Hermann Minkowski Minerva Center for Geometry
High Council for Scientific and Technological Cooperation between France and Israel
Ministry of Science, Israel
Israel Science Foundation
Tel Aviv University


    Dive into the research topics of 'Welschinger invariants of toric Del Pezzo surfaces with nonstandard real structures'. Together they form a unique fingerprint.

    Cite this