The symplectic isotopy problem for rational cuspidal curves

Autor:	Golla, Marco, Starkston, Laura
Rok vydání:	2019
Předmět:	Mathematics - Geometric Topology Mathematics - Algebraic Geometry Mathematics - Symplectic Geometry
Druh dokumentu:	Working Paper
Popis:	We define a suitably tame class of singular symplectic curves in 4-manifolds, namely those whose singularities are modeled on complex curve singularities. We study the corresponding symplectic isotopy problem, with a focus on rational curves with irreducible singularities (rational cuspidal curves) in the complex projective plane. We prove that every such curve is isotopic to a complex curve in degrees up to 5, and for curves with one singularity whose link is a torus knot. Classification results of symplectic isotopy classes rely on pseudo-holomorphic curves together with a symplectic version of birational geometry of log pairs and techniques from 4-dimensional topology. Comment: 78 pages, 45 figures, comments welcome! v3: significant edits to Section 5 (especially Proposition 5.1 and its proof), minor edits elsewhere
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1907.06787 Zobrazit plný text záznamu View this record from Arxiv