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Homogeneous Gorenstein Ideals And Boij Söderberg Decompositions, Sema Güntürkün
Homogeneous Gorenstein Ideals And Boij Söderberg Decompositions, Sema Güntürkün
Theses and Dissertations--Mathematics
This thesis consists of two parts. Part one revolves around a construction for homogeneous Gorenstein ideals and properties of these ideals. Part two focuses on the behavior of the Boij-Söderberg decomposition of lex ideals.
Gorenstein ideals are known for their nice duality properties. For codimension two and three, the structures of Gorenstein ideals have been established by Hilbert-Burch and Buchsbaum-Eisenbud, respectively. However, although some important results have been found about Gorenstein ideals of higher codimension, there is no structure theorem proven for higher codimension cases. Kustin and Miller showed how to construct a Gorenstein ideals in local Gorenstein rings starting …