Automatic Transversality and Orbifolds of Punctured Holomorphic Curves in Dimension Four

Abstract

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.

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

References in corpus (6)

• Geometry of contact transformations and domains: orderability versus squeezing
• Relative asymptotic behavior of pseudoholomorphic half-cylinders
• Intersection theory of punctured pseudoholomorphic curves
• Pseudoholomorphic curves and the symplectic isotopy problem
• The gluing construction for normally generic J-holomorphic curves
• Compactness for Embedded Pseudoholomorphic Curves in 3-manifolds

Cited by in corpus (3)

• Semi-global Kuranishi charts and the definition of contact homology
• Embedding property of $J$-holomorphic curves in Calabi-Yau manifolds for generic $J$
• Open book decompositions and stable Hamiltonian structures