The symplectic isotopy problem for rational cuspidal curves

Marco Golla; Laura Starkston

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arXiv · 1907.06787

The symplectic isotopy problem for rational cuspidal curves

Marco Golla·Laura Starkston

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Abstract

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.

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BibTeX RIS

Marco Golla, Laura Starkston. 2019-07-15. The symplectic isotopy problem for rational cuspidal curves. https://arxiv.org/abs/1907.06787

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