COUNTING REAL J-HOLOMORPHIC DISCS AND SPHERES IN DIMENSION FOUR AND SIX

- Journal title : Journal of the Korean Mathematical Society
- Volume 45, Issue 5, 2008, pp.1427-1442
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2008.45.5.1427

Title & Authors

COUNTING REAL J-HOLOMORPHIC DISCS AND SPHERES IN DIMENSION FOUR AND SIX

Cho, Cheol-Hyun;

Cho, Cheol-Hyun;

Abstract

We provide another proof that the signed count of the real J-holomorphic spheres (or J- holomorphic discs) passing through a generic real configuration of k points is independent of the choice of the real configuration and the choice of J, if the dimension of the Lagrangian submanifold L (fixed point set of involution) is two or three, and also if we assume L is orient able and relatively spin. We also assume that M is strongly semi-positive. This theorem was first proved by Welschinger in a more general setting, and we provide more natural approach using the signed degree of an evaluation map.

Keywords

holomorphic discs;anti-symplectic involution;Welschinger invariants;

Language

English

Cited by

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