Monomial curves, Gorenstein ideals and Stanley decompositions
by Shen, Yihuang, Ph.D., PURDUE UNIVERSITY, 2009, 107 pages; 3379765

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.
 
AdviserBernd Ulrich
SchoolPURDUE UNIVERSITY
SourceDAI/B 70-11, p. , Dec 2009
Source TypeDissertation
SubjectsMathematics
Publication Number3379765
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