Tropical enumerative invariants of F_0 and F_2

Details Tropical enumerative invariants of F_0 and F_2 Tropical enumerative invariants of F_0 and F_2

2008-08-26

arxiv.org/abs/0808.3452v2

Adv. Geom. 11 (2011), no.1, 49-72

Mathematics

Algebraic Geometry

23 pages, corrections to match the published version

Scientific paper

There is an equation relating numbers of curves on F_0 satisfying incidence conditions and numbers of curves on F_2 satisfying incidence conditions. The purpose of this paper is to give a tropical proof of this equation in the case of rational curves. We use induction on the degree and two Kontsevich-type formulas for curves on F_0 and on F_2. The formula for F_2 was not known before and is proved using tropical geometry.

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