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Cones of Hilbert Functions
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0002-9961-383X
2015 (English)In: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247, no 20, 10314-10338 p.Article in journal (Refereed) PublishedText
Abstract [en]

We study the closed convex hull of various collections of Hilbert functions. Working over a standard graded polynomial ring with modules that are generated in degree 0, we describe the supporting hyperplanes and extreme rays for the cones generated by the Hilbert functions of all modules, all modules with bounded alpha-invariant, and all modules with bounded Castelnuovo-Mumford regularity. The first of these cones is infinite-dimensional and simplicial, the second is finite-dimensional but neither simplicial nor polyhedral, and the third is finite-dimensional and simplicial.

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Oxford University Press, 2015. no 20, 10314-10338 p.
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URN: urn:nbn:se:kth:diva-180386DOI: 10.1093/imrn/rnu265ISI: 000366500400015ScopusID: 2-s2.0-84948389776OAI: diva2:894121

QC 20160114

Available from: 2016-01-14 Created: 2016-01-13 Last updated: 2016-01-14Bibliographically approved

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Boij, Mats
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