Spectrum of plane curves via knot theory

Details Spectrum of plane curves via knot theory Spectrum of plane curves via knot theory

2011-01-28

arxiv.org/abs/1101.5471v2

Mathematics

Geometric Topology

22 pages. Corrected the shape of brackets in the formula for signature in Proposition 2.4.2 (a mistake coming from arXiv:1005.

Scientific paper

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.

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