A tropical calculation of the Welschinger invariants of real toric Del Pezzo surfaces

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dc.creatorShustin, E.
dc.date2004-06-06
dc.date2008-03-02
dc.date.accessioned2026-07-07T09:23:55Z
dc.date.available2026-07-07T09:23:55Z
dc.descriptionThe 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.
dc.description38 pages, 3 figures, misprints (which appeared in the published version) in the formulation of the main theorem are corrected as well as in formula (2.12) for the weight of a tropical curve (thanks to a remark by E. Brugalle)
dc.identifierhttps://arxiv.org/abs/math/0406099
dc.identifierhttp://arxiv.org/abs/math/0406099
dc.identifierJ. Algebraic Geom. 15 (2006), no. 2, 285--322
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/155908
dc.subjectAlgebraic Geometry
dc.subjectCombinatorics
dc.subject14H15, 12J25, 14H20, 14M25, 14N10
dc.titleA tropical calculation of the Welschinger invariants of real toric Del Pezzo surfaces
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