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Lyubeznik Ideals Minimally Generated By Four Or Fewer Elements, Nathan S. Fontes
Lyubeznik Ideals Minimally Generated By Four Or Fewer Elements, Nathan S. Fontes
All Theses
Free resolutions for an ideal are constructions that tell us useful information about the structure of the ideal. Every ideal has one minimal free resolution which tells us significantly more about the structure of the ideal. In this thesis, we consider a specific type of resolution, the Lyubeznik resolution, for a monomial ideal I, which is constructed using a total order on the minimal generating set G(I). An ideal is called Lyubeznik if some total order on G(I) produces a minimal Lyubeznik resolution for I. We investigate the problem of characterizing whether an ideal I is Lyubeznik …