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Affine stratifications and equivariant vector bundles on the moduli of principally polarized abelian varieties

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dc.contributor.advisor Grushevsky, Samuel en_US
dc.contributor.author Atyam, Anant en_US
dc.contributor.other Department of Mathematics en_US
dc.date.accessioned 2017-09-20T16:50:09Z
dc.date.available 2017-09-20T16:50:09Z
dc.date.issued 2014-12-01 en_US
dc.identifier.uri http://hdl.handle.net/11401/76388 en_US
dc.description 78 pgs en_US
dc.description.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). en_US
dc.description.sponsorship This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. en_US
dc.format Monograph en_US
dc.format.medium Electronic Resource en_US
dc.language.iso en_US en_US
dc.publisher The Graduate School, Stony Brook University: Stony Brook, NY. en_US
dc.subject.lcsh Mathematics en_US
dc.subject.other Abelian Varieties en_US
dc.title Affine stratifications and equivariant vector bundles on the moduli of principally polarized abelian varieties en_US
dc.type Dissertation en_US
dc.mimetype Application/PDF en_US
dc.contributor.committeemember Lazarsfeld, Robert en_US
dc.contributor.committeemember Starr, Jason en_US
dc.contributor.committeemember Farkas, Gavril en_US

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