Extreme behavior of lex ideals on Betti numbers
Author
Gürdoğan, Hubeyb Üsame
Advisor
Sezer, Müfit
Date
2013Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
This paper mainly deals with the finitely generated graded modules of the polynomial
ring k[x1, x2, ..., xn]. Free resolutions is an important tool to understand
the structure of these modules. Betti numbers are an useful invariant that encodes
the free resolutions. Our concentration accumulates on proving that the lex
ideals provides an upper bound for Betti numbers of the graded ideals with the
same Hilbert function in the polynomial ring k[x1, x2, ..., xn]. The material of this
thesis is contemporary classical and includes the detailed study of the material
that is scattered throughout the sources cited in the bibliography list.