Toric Degenerations, Tropical Curve, and Gromov-Witten Invariants of Fano Manifolds

被引：1

作者：

Nishinou, Takeo ^{[1
]}

机构：

[1] Tohoku Univ, Dept Math, Sendai, Miyagi 980, Japan

来源：

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2015年 / 67卷 / 03期

关键词：

Fano varieties; Gromov-Witten invariants; tropical curves; VARIETIES; SURFACE; MODULI;

D O I：

10.4153/CJM-2014-006-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we give a tropical method for computing Gromov-Witten type invariants of Fano manifolds of special type. This method applies to those Fano manifolds that admit toric degenerations to toric Fano varieties with singularities allowing small resolutions. Examples include (generalized) flag manifolds of type A and some moduli space of rank two bundles on a genus two curve.

引用

页码：667 / 695

页数：29

共 15 条

[1] Cho CH, 2006, ASIAN J MATH, V10, P773
[2] Cox D. A., 1999, Mirror symmetry and algebraic geometry, V68
[3] INVARIANT FUNCTIONS ON LIE-GROUPS AND HAMILTONIAN FLOWS OF SURFACE GROUP-REPRESENTATIONS
GOLDMAN, WM
[J]. INVENTIONES MATHEMATICAE, 1986, 85 (02) : 263 - 302
[4] PSEUDO HOLOMORPHIC-CURVES IN SYMPLECTIC-MANIFOLDS
GROMOV, M
[J]. INVENTIONES MATHEMATICAE, 1985, 82 (02) : 307 - 347
[5] BOHR-SOMMERFELD ORBITS IN THE MODULI SPACE OF FLAT CONNECTIONS AND THE VERLINDE DIMENSION FORMULA
JEFFREY, LC
WEITSMAN, J
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1992, 150 (03) : 593 - 630
[6] Toric degeneration of Schubert varieties and Gelfand-Tsetlin polytopes
Kogan, M
Miller, E
[J]. ADVANCES IN MATHEMATICS, 2005, 193 (01) : 1 - 17
[7] MCDUFF D., 2012, Amer. Math. Soc. Colloq. Publ., V52, DOI [10.1090/coll/052, DOI 10.1090/COLL/052]
[8] Enumerative tropical algebraic geometry in R2
Mikhalkin, G
[J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 18 (02) : 313 - 377
[9] MODULI OF VECTOR BUNDLES ON A COMPACT RIEMANN SURFACE
NARASIMHAN, MS
RAMANAN, S
[J]. ANNALS OF MATHEMATICS, 1969, 89 (01) : 14 - +
[10] NEWSTEAD P. E., 1968, TOPOLOGY, V7, P205

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