Abstract
The Welschinger invariants of real rational algebraic surfaces are natural analogues of the genus zero Gromov-Witten invariants. We establish a tropical formula to calculate the Welschinger invariants of real toric Del Pezzo surfaces for any conjugation-invariant configuration of points. The formula expresses the Welschinger invariants via the total multiplicity of certain tropical curves (non-Archimedean amoebas) passing through generic configurations of points, and then via the total multiplicity of some lattice paths in the convex lattice polygon associated with a given surface. We also present the results of computation of Welschinger invariants, obtained jointly with I. Itenberg and V. Kharlamov.
| Original language | English |
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| Pages (from-to) | 285-322 |
| Number of pages | 38 |
| Journal | Journal of Algebraic Geometry |
| Volume | 15 |
| Issue number | 2 |
| DOIs | |
| State | Published - Apr 2006 |