Free resolutions, combinatorics, and geometry
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2012
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| Online Access: | http://hdl.handle.net/1721.1/73178 |
| _version_ | 1826202385631936512 |
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| author | Sam, Steven V |
| author2 | Richard P. Stanley. |
| author_facet | Richard P. Stanley. Sam, Steven V |
| author_sort | Sam, Steven V |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012. |
| first_indexed | 2024-09-23T12:06:37Z |
| format | Thesis |
| id | mit-1721.1/73178 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T12:06:37Z |
| publishDate | 2012 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/731782019-04-12T20:21:45Z Free resolutions, combinatorics, and geometry Sam, Steven V Richard P. Stanley. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012. This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. Cataloged from student submitted PDF version of thesis. Includes bibliographical references (p. 71-72). Boij-Söderberg theory is the study of two cones: the first is the cone of graded Betti tables over a polynomial ring, and the second is the cone of cohomology tables of coherent sheaves over projective space. Each cone has a triangulation induced from a certain partial order. Our first result gives a module-theoretic interpretation of this poset structure. The study of the cone of cohomology tables over an arbitrary polarized projective variety is closely related to the existence of an Ulrich sheaf, and our second result shows that such sheaves exist on the class of Schubert degeneracy loci. Finally, we consider the problem of classifying the possible ranks of Betti numbers for modules over a regular local ring. by Steven V Sam. Ph.D. 2012-09-26T14:17:56Z 2012-09-26T14:17:56Z 2012 2012 Thesis http://hdl.handle.net/1721.1/73178 809686996 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 72 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Sam, Steven V Free resolutions, combinatorics, and geometry |
| title | Free resolutions, combinatorics, and geometry |
| title_full | Free resolutions, combinatorics, and geometry |
| title_fullStr | Free resolutions, combinatorics, and geometry |
| title_full_unstemmed | Free resolutions, combinatorics, and geometry |
| title_short | Free resolutions, combinatorics, and geometry |
| title_sort | free resolutions combinatorics and geometry |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/73178 |
| work_keys_str_mv | AT samstevenv freeresolutionscombinatoricsandgeometry |