2026-09-18T19:30:27Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/731782022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Richard P. Stanley.
Sam, Steven V
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2012-09-26T14:17:56Z
2012-09-26T14:17:56Z
2012
2012
http://hdl.handle.net/1721.1/73178
809686996
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.
72 p.
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Free resolutions, combinatorics, and geometry
Thesis
application/pdf
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Publication
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