Disk counting on toric varieties via tropical curves

Takeo Nishinou

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

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

Original languageEnglish
Pages (from-to)1423-1472
Number of pages50
JournalAmerican Journal of Mathematics
Volume134
Issue number6
DOIs
Publication statusPublished - 2012 Dec 1

ASJC Scopus subject areas

  • Mathematics(all)

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