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Bounds on Hilbert Functions
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). (Algebraic Geometry)
2013 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is constituted of two articles, both related to Hilbert functions and h-vectors. In the first paper, we deal with h-vectorsof reduced zero-dimensional schemes in the projective plane, and, in particular, with the problem of finding the possible h-vectors for the union of two sets of points of given h-vectors. In the second paper, we generalize the Green’s Hyperplane Restriction Theorem to the case of modules over the polynomial ring.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. , vii, 22 p.
Series
Trita-MAT. MA, ISSN 1401-2278 ; 13:03
Keyword [en]
Hilbert Functions, Commutative Algebra
National Category
Mathematics Algebra and Logic
Identifiers
URN: urn:nbn:se:kth:diva-133942ISBN: 978-91-7501-901-7 (print)OAI: oai:DiVA.org:kth-133942DiVA: diva2:664101
Presentation
2013-11-11, 3418, Lindstedtsvägen 25, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20131114

Available from: 2013-11-14 Created: 2013-11-13 Last updated: 2013-11-14Bibliographically approved
List of papers
1. The h-vector of the union of two sets of points in the projective plane
Open this publication in new window or tab >>The h-vector of the union of two sets of points in the projective plane
2012 (English)In: Le Matematiche, ISSN 2037-5298, E-ISSN 0373-3505, Vol. 67, no 1Article in journal (Refereed) Published
Abstract [en]

Given two h-vectors, handh0, we study which are the possible h-vectors for the union of two disjoint sets of points in P2, respectively associated to h and h0and how they can be constructed. We will give some bounds for the resulting h-vector and we will show how to construct the minimal h-vector of the union among all possible ones.

Keyword
Union, Set, h-vector
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-133985 (URN)10.4418/2012.67.1.16 (DOI)
Note

QC 20131114

Available from: 2013-11-14 Created: 2013-11-14 Last updated: 2017-12-06Bibliographically approved
2. Green’s Hyperplane Restriction Theorem: an extension to modules
Open this publication in new window or tab >>Green’s Hyperplane Restriction Theorem: an extension to modules
2015 (English)In: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 219, no 8, 3506-3517 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we prove a generalization of Green's Hyperplane RestrictionTheorem to the case of modules over the polynomial ring, providing in particularan upper bound for the Hilbert function of the general linear restrictionof a module M in a degree d by the corresponding Hilbert function of alexicographic module.

Keyword
Hilbert function, General linear restriction, Lexicographic modules
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-133986 (URN)10.1016/j.jpaa.2014.12.009 (DOI)000351979000025 ()2-s2.0-84925299702 (Scopus ID)
Note

Updated from manuscript to article.

QC 20150504

Available from: 2013-11-14 Created: 2013-11-14 Last updated: 2017-12-06Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
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More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
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  • asciidoc
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