Some results on perverse sheaves and Bernstein-Sato polynomials /
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| Author / Creator: | Bapat, Asilata, author. |
|---|---|
| Imprint: | 2016. Ann Arbor : ProQuest Dissertations & Theses, 2016 |
| Description: | 1 electronic resource (49 pages) |
| Language: | English |
| Format: | E-Resource Dissertations |
| Local Note: | School code: 0330 |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11674570 |
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| 100 | 1 | |a Bapat, Asilata, |e author. | |
| 245 | 1 | 0 | |a Some results on perverse sheaves and Bernstein-Sato polynomials / |c Bapat, Asilata. |
| 260 | |c 2016. | ||
| 264 | 1 | |a Ann Arbor : |b ProQuest Dissertations & Theses, |c 2016 | |
| 300 | |a 1 electronic resource (49 pages) | ||
| 336 | |a text |b txt |2 rdacontent |0 http://id.loc.gov/vocabulary/contentTypes/txt | ||
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| 500 | |a Advisors: Victor Ginzburg Committee members: Alexander Beilinson. | ||
| 502 | |b Ph.D. |c University of Chicago, Division of the Physical Sciences, Department of Mathematics |d 2016. | ||
| 510 | 4 | |a Dissertation Abstracts International, |c Volume: 77-12(E), Section: B. | |
| 520 | |a The first part of this thesis concerns intersection cohomology sheaves on a smooth projective variety with a torus action that has finitely many fixed points. Under some additional assumptions, we consider tensor products of intersection cohomology sheaves on a Bialynicki-Birula stratification of the variety. We give a formula for the hypercohomology of the tensor product in terms of the tensor products of the individual sheaves, as well as the cohomology of the variety. We prove a similar result in the setting of equivariant cohomology. | ||
| 520 | |a In the second part of this thesis, we study the Bernstein-Sato polynomial, or the b-function, which is an invariant of singularities of hypersurfaces. We are interested in the b-function of hyperplane arrangements of Weyl arrangements, which are the arrangements of root systems of semi-simple Lie algebras. It has been conjectured that the poles of the local topological zeta function, which is another invariant of hypersurface singularities, are all roots of the b-function. Using the work of Opdam and Budur-Mustata-Teitler, we prove this conjecture for all Weyl arrangements. We also give an upper bound for the b-function of the Vandermonde determinant, which cuts out the Weyl arrangement in type A.. | ||
| 546 | |a English | ||
| 590 | |a School code: 0330 | ||
| 690 | |a Mathematics. | ||
| 710 | 2 | |a University of Chicago. |e degree granting institution. |0 http://id.loc.gov/authorities/names/n79058404 |1 http://viaf.org/viaf/143657677 | |
| 720 | 1 | |a Victor Ginzburg |e degree supervisor. | |
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