Rees algebras of modules and Quot schemes of points
2014 (English)Licentiate thesis, comprehensive summary (Other academic)
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.
Algebra and Logic Geometry
Research subject Mathematics
IdentifiersURN: urn:nbn:se:kth:diva-156636ISBN: 978-91-7595-400-4OAI: oai:DiVA.org:kth-156636DiVA: diva2:769721
2015-01-23, 3418, Lindstedtsvägen 25, Stockholm, 10:00 (English)
Skjelnes, Roy, UniversitetslektorRydh, David, Universitetslektor
QC 201412182014-12-182014-12-012014-12-18Bibliographically approved
List of papers