Automatic Transversality and Orbifolds of Punctured Holomorphic Curves in Dimension Four

Details Automatic Transversality and Orbifolds of Punctured Holomorphic Curves in Dimension Four Automatic Transversality and Orbifolds of Punctured Holomorphic Curves in Dimension Four

2008-02-26

arxiv.org/abs/0802.3842v4

Mathematics

Symplectic Geometry

58 pages; v.4 replaces the proof of Lemma 3.3 with one that is not obviously wrong; to appear in Comment. Math. Helv

Scientific paper

We derive a numerical criterion for J-holomorphic curves in 4-dimensional symplectic cobordisms to achieve transversality without any genericity assumption. This generalizes results of Hofer-Lizan-Sikorav and Ivashkovich-Shevchishin to allow punctured curves with boundary that generally need not be somewhere injective or immersed. As an application, we combine this with the intersection theory of punctured holomorphic curves to prove that certain geometrically natural moduli spaces are globally smooth orbifolds, consisting generically of embedded curves, plus unbranched multiple covers that form isolated orbifold singularities.

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