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.
Author: | Nguyen Khanh Linh Tran |
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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): | Standardbedingung laut Einverständniserklärung |