On the local version of the Severi problem

Details On the local version of the Severi problem On the local version of the Severi problem

2002-07-04

arxiv.org/abs/math/0207048v1

Mathematics

Algebraic Geometry

33 pages, AMS-LaTeX, no figures

Scientific paper

For a given singularity of a plane curve we consider the locus of nodal deformations of the singularity with the given number of nodes and describe possible components of the locus. As applications, we solve the local symplectic isotopy for nodal curves in a neighborhood of a given pseudoholomorphic curve without multiple components and prove the uniqueness of the symplectic isotopy class for nodal pseudoholomorphic curves of low genus in $\CP^2$ and $\CP^2 # \bar\CP^2$.

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