Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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COUNTING REAL J-HOLOMORPHIC DISCS AND SPHERES IN DIMENSION FOUR AND SIX

  • Cho, Cheol-Hyun (Department of Mathematical Sciences Seoul National University)
  • Published : 2008.09.30
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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.

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References

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