2011/05/27 by Matteo Varbaro, Varbaro, Matteo
Mathematics · #05E10 #05E40 #13A15 #13A50 #13D45 #13F50 #13F55 #13H10 #13P10 #14B15 #14F20 #14M10 #14M99 #20G05 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT) #math.AC #math.AG #math.CO #math.RT #msc:05E10 #msc:05E40 #msc:13A15 #msc:13A50 #msc:13D45 #msc:13F50 #msc:13F55 #msc:13H10 #msc:13P10 #msc:14B15 #msc:14F20 #msc:14M10 #msc:14M99 #msc:20G05
paper · pdf · doi:10.48550/arxiv.1105.5507
This is the PhD thesis of the author. Most of the results appeared (or are going to appear) in some paper. However throughout the thesis there are also unpublished results, proofs and remarks
arxiv created 2011/05/27 · openalex publication_date 2011/05/27 · arxiv updated 2011/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this PhD thesis we will discuss some aspects in Commutative Algebra which have interactions with Algebraic Geometry, Representation Theory and Combinatorics. In particular, in the first chapter we will focus on understanding when certain cohomology modules vanish, a classical problem raised by Grothendieck. In the second chapter we will use local cohomology to study the connectedness behavior during a Groebner deformation and the arithmetical rank of certain varieties. In the third chapter, we will investigate the relations between the minors of a fixed size of a generic matrix by using tools from the representation theory of the general linear group (the results of this chapter will appear in a joint paper with Bruns and Conca). In the last chapter we will use combinatorial methods to study the Cohen-Macaulay property of the symbolic powers of Stanley-Reisner ideals. In the thesis are included five appendixes with some basic needed facts and a preliminary chapter introducing to local cohomology.