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Kaehler Differential Algebras for 0-Dimensional Schemes and Applications

  • The aim of this dissertation is to investigate Kaehler differential algebras and their Hilbert functions for 0-dimensional schemes in P^n. First we give relations between Kaehler differential 1-forms of fat point schemes and another fat point schemes. Then we determine the Hilbert polynomial and give a sharp bound for the regularity index of the module of Kaehler differential m-forms, for 0<m<n+2. Next, we examine the Kaehler differential algebras for fat point schemes whose supports lie on non-singular conics in P^2. Finally, we prove the Segre bounds for equimultiple fat point schemes in P^4, this result allows us to determine the regularity index of the module of Kaehler differential 1-forms, and a sharp bound for the regularity index of the module of Kaehler differential m-forms, for 1<m<6.

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Author:Nguyen Khanh Linh Tran
URN:urn:nbn:de:bvb:739-opus4-3290
Advisor:Martin Kreuzer
Document Type:Doctoral Thesis
Language:English
Year of Completion:2015
Date of Publication (online):2015/11/16
Date of first Publication:2015/11/16
Publishing Institution:Universität Passau
Granting Institution:Universität Passau, Fakultät für Informatik und Mathematik
Date of final exam:2015/10/23
Release Date:2015/11/16
GND Keyword:Kähler-Differentialform
Page Number:158
Institutes:Fakultät für Informatik und Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
open_access (DINI-Set):open_access
Licence (German):License LogoStandardbedingung laut Einverständniserklärung