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.
Committee Chair
Matt Kerr
Degree
Doctor of Philosophy (PhD)
Author's Department
Mathematics
Document Type
Dissertation
Date of Award
4-27-2022
Language
English (en)
DOI
https://doi.org/10.7936/e5q9-6v92
Recommended Citation
Castor, Benjamin, "Bounding Projective Hypersurface Singularities" (2022). Arts & Sciences Theses and Dissertations. 3255.
The definitive version is available at https://doi.org/10.7936/e5q9-6v92