ArchivIA Università degli Studi di Catania
 

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

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10761/4114

Data: 2-feb-2019
Autori: Picone, Concetta Maria Beatrice
Titolo: 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.
InArea 01 - Scienze matematiche e informatiche

Full text:

File Descrizione DimensioniFormatoConsultabilità
PCNCCT91C53C351A.pdf51,04 MBAdobe PDFVisualizza/apri


Tutti i documenti archiviati in ArchivIA sono protetti da copyright. Tutti i diritti riservati.


Segnala questo record su
Del.icio.us

Citeulike

Connotea

Facebook

Stumble it!

reddit


 

  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.