Automatic Transversality and Orbifolds of Punctured Holomorphic Curves in Dimension Four

2008/02/26 by Wendl, Chris · 3 citations
#32Q65 #57R17 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.0802.3842

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.

Cited by

• Lectures on stabilized ellipsoid embeddings
• Refined Elementary Capacities from Symplectic Field Theory
• Quadratic growth of geodesics on the two-sphere

Related

• Nongeneric J-holomorphic curves in symplectic 4-manifolds
• Pseudoholomorphic curves in four-orbifolds and some applications
• Punctured holomorphic curves and Lagrangian embeddings
• Generic transversality for unbranched covers of closed pseudoholomorphic curves
• Transversality and super-rigidity for multiply covered holomorphic curves