Date of Award
4-27-2022
Degree Name
Doctor of Philosophy (PhD)
Degree Type
Dissertation
Abstract
We first provide background necessary for understanding monodromy and spectra. We then compare several different methods involving Hodge-theoretic spectra of singularities which produce constraints on the number and type of isolated singularities on a projective hypersurface of fixed degree. In particular, we introduce a method based on the spectrum of the nonisolated singularity at the origin of the affine cone on such a hypersurface, and relate the resulting explicit formula to Varchenko’s bound. We then provide a purely combinatorial interpretation of our theorems and our conjecture.
Language
English (en)
Chair and Committee
Matt Kerr
Recommended Citation
Castor, Benjamin, "Bounding Projective Hypersurface Singularities" (2022). Arts & Sciences Electronic Theses and Dissertations. 3255.
https://openscholarship.wustl.edu/art_sci_etds/3255