Mathematics – Algebraic Geometry
Scientific paper
2004-06-06
J. Algebraic Geom. 15 (2006), no. 2, 285--322
Mathematics
Algebraic Geometry
38 pages, 3 figures, misprints (which appeared in the published version) in the formulation of the main theorem are corrected
Scientific paper
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 path 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.
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