Welschinger invariants of toric Del Pezzo surfaces with non-standard real structures

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dc.creatorShustin, E.
dc.date2006-05-27
dc.date.accessioned2026-07-07T07:14:34Z
dc.date.available2026-07-07T07:14:34Z
dc.descriptionThe Welschinger invariants of real rational algebraic surfaces are natural analogues 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 non-standard 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 surfaces $Σ$ under consideration, through any generic configuration of $c_1(Σ)D-1$ generic real points there passes a real rational curve belonging to the linear system $|D|$.
dc.descriptionAn extended version of MPI Preprint no. MPIM2005-44
dc.identifierhttps://arxiv.org/abs/math/0605697
dc.identifierhttp://arxiv.org/abs/math/0605697
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112924
dc.subjectAlgebraic Geometry
dc.subjectCommutative Algebra
dc.subjectPrimary 14H15. Secondary 12J25, 14H20, 14M25, 14N10
dc.titleWelschinger invariants of toric Del Pezzo surfaces with non-standard real structures
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