Type
Text
Type
Dissertation
Advisor
Lazarsfeld, Robert | Grushevsky, Samuel | Starr, Jason | Farkas, Gavril.
Date
2014-12-01
Keywords
Mathematics | Abelian Varieties
Department
Department of Mathematics.
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/76388
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
We explicitly construct a locally closed affine stratification of the coarse moduli space of principally polarized abelian four folds A4 over the complex numbers and using the work of Roth and Vakil, produce an upper bound for the coherent cohomological dimension and the constructible cohomological dimension of A4. Based on the work of Oort and Van Der Geer, we make a conjecture on the cohomological dimension of the moduli stack Ag for all g. In the second part of the thesis we study the ring of equivariant vector bundles on Ag and study the chern character map from this ring to the tautological ring of Ag. We give a conjectural representation theoretic interpretation of the tautological ring of Ag as a shifted quotient of the representation ring of GL(g,C) by the representation ring of Sp(2g,C). | 78 pages
Recommended Citation
Atyam, Anant, "Affine stratifications and equivariant vector bundles on the moduli of principally polarized abelian varieties" (2014). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 2311.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/2311