Disc counting on toric varieties via tropical curves

Details Disc counting on toric varieties via tropical curves Disc counting on toric varieties via tropical curves

2006-10-22

arxiv.org/abs/math/0610660v2

Mathematics

Algebraic Geometry

Revised version

Scientific paper

In this paper, we define two numbers. One comes from counting tropical curves with a stop and the other is the number of holomorphic discs in toric varieties with Lagrangian boundary condition. Both of these curves should satisfy some matching conditions. We show that these numbers coincide. These numbers can be considered as Gromov-Witten type invariants for holomorphic discs, and they have both similarities and differences to the counting numbers of closed holomorphic curves. We study several aspects of them.

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