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

We provide another proof that the signed count of the real Jholomorphic 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...

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Bibliographic Details
Published inJournal of the Korean Mathematical Society Vol. 45; no. 5; pp. 1427 - 1442
Main Author Cho, Cheol-Hyun
Format Journal Article
LanguageEnglish
Published 대한수학회 01.09.2008
Subjects
수학
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Summary:We provide another proof that the signed count of the real Jholomorphic 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 orientable 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. KCI Citation Count: 16
Bibliography:G704-000208.2008.45.5.002
ISSN:0304-9914
2234-3008
DOI:10.4134/JKMS.2008.45.5.1427