Spectrum of plane curves via knot theory

Maciej Borodzik; Andras Nemethi

doi:10.1112/jlms/jdr078

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arXiv · 1101.5471

Spectrum of plane curves via knot theory

Maciej Borodzik·Andras Nemethi

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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.

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Maciej Borodzik, Andras Nemethi. 2011-05-24. Spectrum of plane curves via knot theory. https://doi.org/10.1112/jlms%2Fjdr078

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