Recursive Formulas for Welschinger Invariants of the Projective Plane

被引：23

作者：

Arroyo, Aubin ^{[1
]}

Brugalle, Erwan ^{[2
]}

Lopez de Medrano, Lucia ^{[1
]}

机构：

[1] Univ Nacl Autonoma Mexico, Inst Matemat, Unidad Cuernavaca, Cuernavaca 62251, Morelos, Mexico

[2] Univ Paris 06, F-75013 Paris, France

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2011年 / 2011卷 / 05期

关键词：

SYMPLECTIC; 4-MANIFOLDS; LOWER BOUNDS; CURVES;

D O I：

10.1093/imrn/rnq096

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Welschinger invariants of the real projective plane can be computed via the enumeration of enriched graphs, called marked floor diagrams. By a purely combinatorial study of these objects, we establish a Caporaso-Harris type formula which allows one to compute Welschinger invariants for configurations of points with any number of complex conjugated points.

引用

页码：1107 / 1134

页数：28

共 17 条

[1] Brugalle E., 2008, P 15 GOK GEOM TOP C, P64
[2] Brugalle E., FLOOR DECOMPOS UNPUB
[3] Enumeration of curves via floor diagrams
Brugalle, Erwan
Mikhalkin, Grigory
[J]. COMPTES RENDUS MATHEMATIQUE, 2007, 345 (06) : 329 - 334
[4] Counting plane curves of any genus
Caporaso, L
Harris, J
[J]. INVENTIONES MATHEMATICAE, 1998, 131 (02) : 345 - 392
[5] DIFRANCESCO P, 1994, PROGR MATH, V129, P81
[6] The Caporaso-Harris formula and plane relative Gromov-Witten invariants in tropical geometry
Gathmann, Andreas
Markwig, Hannah
[J]. MATHEMATISCHE ANNALEN, 2007, 338 (04) : 845 - 868
[7] Logarithmic equivalence of Welschinger and Gromov-Witten invariants
Itenberg, I
Kharlamov, V
Shustin, E
[J]. RUSSIAN MATHEMATICAL SURVEYS, 2004, 59 (06) : 1093 - 1116
[8] Itenberg I, 2003, INT MATH RES NOTICES, V2003, P2639
[9] Itenberg I, 2009, COMMENT MATH HELV, V84, P87
[10] GORMOV-WITTEN CLASSES, QUANTUM COHOMOLOGY, AND ENUMERATIVE GEOMETRY
KONTSEVICH, M
MANIN, Y
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1994, 164 (03) : 525 - 562

← 1 2 →