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Bounds on Hilbert Functions and Betti Numbers of Veronese ModulesPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2014 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Stockholm: KTH Royal Institute of Technology, 2014. , vii, 31 p.
##### Series

TRITA-MAT-A, 2014:16
##### Keyword [en]

Hilbert function, Betti numbers, Veronese modules, Pinched veronese, h-vectors
##### National Category

Algebra and Logic Geometry
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-158913ISBN: 978-91-7595-394-6 (print)OAI: oai:DiVA.org:kth-158913DiVA: diva2:780001
##### Public defence

2015-02-04, F3, Lindstedtsvägen 26, KTH, Stockholm, 14:00 (English)
##### Opponent

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##### Note

##### List of papers

The thesis is a collection of four papers dealing with Hilbert functions and Betti numbers.In the first paper, we study the h-vectors of reduced zero-dimensional schemes in . In particular we deal with the problem of findingthe possible h-vectors for the union of two sets of points of given h-vectors. To answer to this problem, we give two kinds of bounds on theh-vectors and we provide an algorithm that calculates many possibleh-vectors.In the second paper, we prove a generalization of Green’s Hyper-plane Restriction Theorem to the case of finitely generated modulesover the polynomial ring, providing an upper bound for the Hilbertfunction of the general linear restriction of a module M in a degree dby the corresponding Hilbert function of a lexicographic module.In the third paper, we study the minimal free resolution of theVeronese modules, , where by giving a formula for the Betti numbers in terms of the reduced homology of the squarefree divisor complex. We prove that is Cohen-Macaulay if and only if k < d, and that its minimal resolutionis linear when k > d(n − 1) − n. We prove combinatorially that the resolution of is pure. We provide a formula for the Hilbert seriesof the Veronese modules. As an application, we calculate the completeBetti diagrams of the Veronese rings .In the fourth paper, we apply the same combinatorial techniques inthe study of the properties of pinched Veronese rings, in particular weshow when this ring is Cohen-Macaulay. We also study the canonicalmodule of the Veronese modules.

QC 20150115

Available from: 2015-01-15 Created: 2015-01-13 Last updated: 2015-01-15Bibliographically approved1. The h-vector of the union of two sets of points in the projective plane$(function(){PrimeFaces.cw("OverlayPanel","overlay664163",{id:"formSmash:j_idt482:0:j_idt486",widgetVar:"overlay664163",target:"formSmash:j_idt482:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Green’s Hyperplane Restriction Theorem: an extension to modules$(function(){PrimeFaces.cw("OverlayPanel","overlay664166",{id:"formSmash:j_idt482:1:j_idt486",widgetVar:"overlay664166",target:"formSmash:j_idt482:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Syzygies of Veronese modules$(function(){PrimeFaces.cw("OverlayPanel","overlay779975",{id:"formSmash:j_idt482:2:j_idt486",widgetVar:"overlay779975",target:"formSmash:j_idt482:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Cohen-Macaulay Property of pinched Veronese Rings and Canonical Modules of Veronese Modules$(function(){PrimeFaces.cw("OverlayPanel","overlay779980",{id:"formSmash:j_idt482:3:j_idt486",widgetVar:"overlay779980",target:"formSmash:j_idt482:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

isbn
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