A Caporaso-Harris type formula for Welschinger invariants of real toric Del Pezzo surfaces

By I. Itenberg, Viatcheslav Kharlamov, Eugenii Shustin. 2006

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We define a series of relative tropical Welschinger-type invariants of real toric surfaces. In the Del Pezzo case, these invariants can be seen as real tropical analogs of relative Gromov�Witten invariants, and are subject to a recursive formula. As application we obtain new formulas for Welschinger invariants of real toric Del Pezzo surfaces.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/373d3ecca466f91b4767367eaf783b631e324b79

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In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

On Block-Goettsche multiplicities for planar tropical curves (2012, background): “It was found in [10] that the expression (1.”
Welschinger invariants of real Del Pezzo surfaces of degree ≥ 3 (2011, methodology): “ of disjoint (−1)-curves such that DE ′= DE ′= 0, we blow down both E and E and obtain a surface of one of the types P2 a′,b′, a ′ + 2b′ ≤ 4, b′ ≤ 1, for which the relations (22) and (20) follow from [8, 9, 11, 12, 13, 17]. Thus, suppose that Dintersects with each imaginary (−1)-curve, and that ther”
Refined curve counting on complex surfaces (2012, methodology): “The Caporaso-Harris formula has been derived tropically by Gathmann and Markwig [GM], and an analogue for the tropical Welschinger invariants by Itenberg, Kharlamov, and Shustin [IKS].”
Floor diagrams relative to a conic, and GW-W invariants of Del Pezzo surfaces (2014, background): “Furthermore in the case of X3, the numbers I obtained in this way are the corresponding tropical Welschinger invariants (see [IKS09] for a definition).”