Spectrum of plane curves via knot theory
Geometric Topology
2014-02-26 v2 Algebraic Geometry
Abstract
We use topological methods to study various semicontinuity properties of spectra of singular points of plane algebraic curves and of polynomials in two variables at infinity. Using Seifert forms and the Tristram--Levine signatures of links, we reprove (in a slightly weaker version) a result obtained by Steenbrink and Varchenko on semicontinuity of spectrum at infinity. We also relate the spectrum at infinity of a polynomial with spectra of singular points of a chosen fiber.
Keywords
Cite
@article{arxiv.1101.5471,
title = {Spectrum of plane curves via knot theory},
author = {Maciej Borodzik and Andras Nemethi},
journal= {arXiv preprint arXiv:1101.5471},
year = {2014}
}
Comments
22 pages. Corrected the shape of brackets in the formula for signature in Proposition 2.4.2 (a mistake coming from arXiv:1005.2084). A few other statements on page 6 slightly changed, otherwise no changes needed