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COUNTING REAL J-HOLOMORPHIC DISCS AND SPHERES IN DIMENSION FOUR AND SIX
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 Title & Authors
COUNTING REAL J-HOLOMORPHIC DISCS AND SPHERES IN DIMENSION FOUR AND SIX
Cho, Cheol-Hyun;
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 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
1.
Open Gromov–Witten invariants in dimension six, Mathematische Annalen, 2013, 356, 3, 1163  crossref(new windwow)
2.
Localization Computation of One-Point Disk Invariants of Projective Calabi–Yau Complete Intersections, Communications in Mathematical Physics, 2014, 332, 2, 885  crossref(new windwow)
3.
Open Gromov–Witten disk invariants in the presence of an anti-symplectic involution, Advances in Mathematics, 2016, 301, 116  crossref(new windwow)
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