TY - JOUR
T1 - Disk counting on toric varieties via tropical curves
AU - Nishinou, Takeo
PY - 2012/12/1
Y1 - 2012/12/1
N2 - 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.
AB - 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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U2 - 10.1353/ajm.2012.0043
DO - 10.1353/ajm.2012.0043
M3 - Article
AN - SCOPUS:84870308845
VL - 134
SP - 1423
EP - 1472
JO - American Journal of Mathematics
JF - American Journal of Mathematics
SN - 0002-9327
IS - 6
ER -