Multivariable Hodge theoretical invariants of germs of plane curves
Pierrette Cassou-Nogues, Anatoly Libgober
TL;DR
This paper introduces methods to compute polytopes of quasiadjunction for plane curve singularities, providing a Hodge-theoretic refinement of multivariable Alexander polynomial zero sets and identifying key hyperplanes related to Bernstein ideals.
Contribution
It presents novel computational techniques for polytopes of quasiadjunction, linking Hodge theory with multivariable Alexander invariants of plane curve singularities.
Findings
Identification of hyperplanes where multivariable Bernstein polynomials vanish
Development of methods for calculating polytopes of quasiadjunction
Refinement of invariants using Hodge theory
Abstract
We describe methods for calculation of polytopes of quasiadjunction for plane curve singularities which are invariants giving a Hodge theoretical refinement of the zero sets of multivariable Alexander polynomials. In particular we identify some hyperplanes on which all polynomials in multivariable Bernstein ideal vanish.
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