Tropical invariants from the secondary fan
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Eric Katz
Abstract
In this paper, we consider weighted counts of tropical plane curves of particular combinatorial type through a certain number of generic points. We give a criterion, effectively balancing, derived from tropical intersection theory on the secondary fan, for a weighted count to give a number invariant of the position of the points. By computing a certain intersection multiplicity, we determine which weighted counts in our approach replicates Mikhalkin's computation of Gromov–Witten invariants although we do not know if such a count is effectively balanced. This begins to address a question raised by Dickenstein, Feichtner, and Sturmfels. We also give a geometric interpretation of the numbers we produce involving Chow quotients, and provide a counterexample showing that the tropical Severi variety is not always supported on the secondary fan.
© de Gruyter 2009
Articles in the same Issue
- Tropical invariants from the secondary fan
- Quotients of projective spaces and spheres
- Gauss curvature flow on surfaces of revolution
- Stringy E-functions of hypersurfaces and of Brieskorn singularities
- Relations for virtual fundamental classes of Hilbert schemes of curves on surfaces
- The classification of surfaces with pg = q = 1 isogenous to a product of curves
- Some quasihomogeneous Legendrian varieties
- Families of surfaces and conjugate curve congruences
Articles in the same Issue
- Tropical invariants from the secondary fan
- Quotients of projective spaces and spheres
- Gauss curvature flow on surfaces of revolution
- Stringy E-functions of hypersurfaces and of Brieskorn singularities
- Relations for virtual fundamental classes of Hilbert schemes of curves on surfaces
- The classification of surfaces with pg = q = 1 isogenous to a product of curves
- Some quasihomogeneous Legendrian varieties
- Families of surfaces and conjugate curve congruences
