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http://dx.doi.org/10.4134/JKMS.2008.45.5.1427

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

Cho, Cheol-Hyun (Department of Mathematical Sciences Seoul National University)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.5, 2008 , pp. 1427-1442 More about this Journal
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;
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