A tropical calculation of the Welschinger invariants of real toric Del Pezzo surfaces
By Eugenii Shustin. 2004
59 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/354b59cd2ebaf280fc9cbfc5f60d8467e7fc428a
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
- Erwan Brugallé
- Eugenii Shustin
- I. Itenberg
- Viatcheslav Kharlamov
- G. Mikhalkin
- Eric Katz
- Ilya Tyomkin
- O. Y. Viro
In Computational Theory and Mathematics
- Erwan Brugallé
- Eugenii Shustin
- I. Itenberg
- Viatcheslav Kharlamov
- G. Mikhalkin
- Eric Katz
- Ilya Tyomkin
- L. Gottsche
In Geometry and Topology
- I. Itenberg
- Erwan Brugallé
- Eugenii Shustin
- Viatcheslav Kharlamov
- G. Mikhalkin
- Jean-Yves Welschinger
- Ilya Tyomkin
- Eric Katz
Citations in the corpus
- Floor decompositions of tropical curves : the planar case (2008, methodology): “o R r+oCr Y v∈Vert(ℑ(Ce)/φ) µC(v,f) Y v∈Vert(Ce), f(v)∈ωr µC(v,f) Y v∈Vert(Ce), v is 4-valent µR(v,f) The tropical curves and their multiplicity we are considering here differ slightly from the one in [Shu06]. This difference comes from the fact that we are dealing with parameterization of tropical cu”
- Logarithmic equivalence of Welschinger and Gromov-Witten invariants (2004, background): “Shustin [6, 7], we studied the toric unnodal Del Pezzo surfaces with tautological real structure and showed that for these surfaces Welschinger and Gromov-Witten invariants are equivalent in the logarithmic scale, if all or almost all fixed points in the generic collection are real.”