ArchivIA Università degli Studi di Catania

ArchivIA - Archivio istituzionale dell'Universita' di Catania >
Tesi >
Tesi di dottorato >
Area 01 - Scienze matematiche e informatiche >

Please use this identifier to cite or link to this item:

Issue Date: 2-Feb-2019
Authors: Picone, Concetta Maria Beatrice
Title: Homological invariants of some special varieties
Abstract: In this PhD thesis, we discuss several different results about some homological invariants (e.g., graded Betti numbers, Hilbert function, regularity) of some special varieties. In particular, we focus on the codimension two ACM varieties in P1×P1×P1 (called varieties of lines), and the edge ideals of bicyclic graphs. We study the Hilbert function of Ferrers varieties of lines, a special case of ACM variety of lines, and we describe the trigraded minimal free resolution of the defining ideal of a variety of lines arising from a complete intersection of points. We also compute the Castelnuovo-Mumford regularity of the defining ideal of grids of lines and complete intersections of lines in P1×P1×P1. Then we study the regularity of another special variety, i.e., the edge ideal of a bicyclic graph and its powers. Specifically, we compute the regularity of the edge ideal of a dumbbell graph, and then we give a combinatorial characterization of the regularity of the edge ideal of an arbitrary bicyclic graph in terms of its induced matching number. Finally we study the regularity of powers of edge ideals of some specific bicyclic graphs, i.e., dumbbell graphs with path having at most two vertices.
Appears in Collections:Area 01 - Scienze matematiche e informatiche

Files in This Item:

File Description SizeFormatVisibility
PCNCCT91C53C351A.pdf51,04 MBAdobe PDFView/Open

Items in ArchivIA are protected by copyright, with all rights reserved, unless otherwise indicated.

Share this record




Stumble it!



  Browser supportati Firefox 3+, Internet Explorer 7+, Google Chrome, Safari

ICT Support, development & maintenance are provided by the AePIC team @ CILEA. Powered on DSpace Software.