Papers

Peer-reviewed
Dec, 2012

DISK COUNTING ON TORIC VARIETIES VIA TROPICAL CURVES

AMERICAN JOURNAL OF MATHEMATICS
  • Takeo Nishinou

Volume
134
Number
6
First page
1423
Last page
1472
Language
English
Publishing type
Research paper (scientific journal)
Publisher
JOHNS HOPKINS UNIV PRESS

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.

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Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000320010400001&DestApp=WOS_CPL
ID information
  • ISSN : 0002-9327
  • Web of Science ID : WOS:000320010400001

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