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      • HARVEST
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      Grobner bases via linkage for classes of generalized determinantal ideals

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      NEYE-DISSERTATION-2022.pdf (1.026Mb)
      Date
      2022-04-12
      Author
      Neye, Emmanuel O
      ORCID
      0000-0003-1201-754X
      Type
      Thesis
      Degree Level
      Doctoral
      Metadata
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      Abstract
      Grobner bases are an important tool for working with ideals in polynomial rings. They have both computational and theoretical importance. In this dissertation, we produce Grobner bases for some families of generalized determinantal ideals. Our main contribution is a Grobner basis for Schubert patch ideals. Schubert patch ideals are prime defining ideals of open patches of Schubert varieties in the type A flag variety. We adapt E. Gorla, J. Migliore, and U. Nagel's "Grobner basis via linkage" technique to prove a conjecture of A. Yong, namely, the essential minors of every Schubert patch ideal form a Grobner basis. Using the same approach, we recover the result of A. Woo and A. Yong that the essential minors of a Kazhdan-Lusztig ideal (and hence, essential minors of a Schubert determinantal ideal) form a Grobner basis with respect to an appropriate term order. In addition, with respect to the standard grading, we show that homogeneous Schubert patch ideals, homogeneous Kazhdan-Lusztig ideals and Schubert determinantal ideals are glicci. In the last chapter of this dissertation, we briefly discuss some future directions.
      Degree
      Doctor of Philosophy (Ph.D.)
      Department
      Mathematics and Statistics
      Program
      Mathematics
      Supervisor
      Rajchgot, Jenna
      Committee
      Rayan, Steven; Franc, Cameron; Szafron, Michael; Wang, Jiun-Chau
      Copyright Date
      April 2022
      URI
      https://hdl.handle.net/10388/13942
      Subject
      Grobner basis
      Schubert patch ideal
      Kazhdan-Lusztig ideal
      Schubert determinantal ideal
      Schubert varieties
      Glicci
      Vertex decomposable
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