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      Generic initial ideals of modular polynomial invariants

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      Author(s)
      Danış, Bekir
      Advisor
      Sezer, Müfit
      Date
      2020-07
      Publisher
      Bilkent University
      Language
      English
      Type
      Thesis
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      Abstract
      We study the generic initial ideals (gin) of certain ideals that arise in modular invariant theory. For all the cases where an explicit generating set is known, we calculate the generic initial ideal of the Hilbert ideal of a cyclic group of prime order for all monomial orders. We also clarify gin for the Klein four group and note that its Hilbert ideals are Borel fixed with certain orderings of the variables. In all the situations we consider, there is a monomial order such that the gin of the Hilbert ideal is equal to its initial ideal. Along the way we show that gin respects a permutation of the variables in the monomial order.
      Keywords
      Generic initial ideals
      Modular polynomial invariants
      Permalink
      http://hdl.handle.net/11693/53927
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      • Dept. of Mathematics - Ph.D. / Sc.D. 48
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