Free resolutions, combinatorics, and geometry
Name
809686996-MIT.pdf
Description
Full printable version
Size
714.91 KB
Format
Adobe PDF
Checksum (MD5)
5e54483a80f50b31e06b2cae90d27580
Author(s)
Sam, Steven V
Advisor(s)
Richard P. Stanley.
Date Issued
2012
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
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).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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