Monomial curves, Gorenstein ideals and Stanley decompositions
Abstract
This thesis is divided into three parts. In the first part, we investigate the defining ideals of numerical semigroup rings of small embedding dimension. Using the corresponding initial ideal, we find explicit descriptions of Buchsbaum, Cohen-Macaulay and/or Gorenstein properties of the tangent cone at the maximal ideal. In the second part, we revisit the Buchsbaum-Eisenbud structure theorem for Gorenstein ideals. If I is a Gorenstein ideal of grade 3, it has a free resolution [special characters omitted] characterized by this structure theorem, in terms of Pfaffians. Under a mild condition, we show that the "initial part" of [special characters omitted] gives a free resolution of the "initial part" of I. In the third and last part, we study the Stanley decomposition of several types of squarefree monomial ideals. Stanley depths for these ideals are conjectured, estimated and/or determined.
Degree
Ph.D.
Advisors
Ulrich, Purdue University.
Subject Area
Mathematics
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