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Rees algebras of modules and Quot schemes of points
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0001-8893-5211
2014 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of three articles. The first two concern a generalization of Rees algebras of ideals to modules. Paper A shows that the definition of the Rees algebra due to Eisenbud, Huneke and Ulrich has an equivalent, intrinsic, definition in terms of divided powers. In Paper B, we use coherent functors to describe properties of the Rees algebra. In particular, we show that the Rees algebra is induced by a canonical map of coherent functors.

In Paper C, we prove a generalization of Gotzmann's persistence theorem to finite modules. As a consequence, we show that the embedding of the Quot scheme of points into a Grassmannian is given by a single Fitting ideal.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2014. , vii, 19 p.
Series
TRITA-MAT-A, 2014:17
National Category
Algebra and Logic Geometry
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-156636ISBN: 978-91-7595-400-4 (print)OAI: oai:DiVA.org:kth-156636DiVA: diva2:769721
Presentation
2015-01-23, 3418, Lindstedtsvägen 25, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20141218

Available from: 2014-12-18 Created: 2014-12-01 Last updated: 2014-12-18Bibliographically approved
List of papers
1. An intrinsic definition of the Rees algebra of a module
Open this publication in new window or tab >>An intrinsic definition of the Rees algebra of a module
(English)In: Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, E-ISSN 1464-3839Article in journal (Refereed) Accepted
Abstract [en]

This paper concerns a generalization of the Rees algebra of ideals due to Eisenbud, Huneke and Ulrich that works for any finitely generated module over a noetherian ring. Their definition is in terms of maps to free modules. We give an intrinsic definition using divided powers.

National Category
Algebra and Logic
Research subject
Mathematics
Identifiers
urn:nbn:se:kth:diva-156533 (URN)
Note

QCR 20161110

Available from: 2014-12-01 Created: 2014-11-29 Last updated: 2017-12-05Bibliographically approved
2. Rees algebras of modules and coherent functors
Open this publication in new window or tab >>Rees algebras of modules and coherent functors
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We show that several properties of the theory of Rees algebras of modules become more transparent using the category of coherent functors rather than working directly with modules. In particular, we show that the Rees algebra is induced by a canonical map of coherent functors.

National Category
Algebra and Logic
Research subject
Mathematics
Identifiers
urn:nbn:se:kth:diva-156534 (URN)
Note

QCR 20161110

Available from: 2014-12-01 Created: 2014-11-29 Last updated: 2016-11-10Bibliographically approved
3. Gotzmann's persistence theorem for finite modules
Open this publication in new window or tab >>Gotzmann's persistence theorem for finite modules
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We prove a generalization of Gotzmann's persistence theorem in the case of modules with constant Hilbert polynomial. As a consequence, we show that the defining equations that give the embedding of a Quot scheme of points into a Grassmannian are given by a single Fitting ideal.

National Category
Algebra and Logic Geometry
Research subject
Mathematics
Identifiers
urn:nbn:se:kth:diva-156535 (URN)
Note

QCR 20161110

Available from: 2014-12-01 Created: 2014-11-29 Last updated: 2016-11-10Bibliographically approved

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