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The relative canonical algebra for genus 3 fibrations
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Lopes, Margarida Mendes (1988) The relative canonical algebra for genus 3 fibrations. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b1455053~S1
Abstract
This thesis studies surfaces with fibrations by curves of small genus, usually locally in a neighbourhood of a singular fibre. The main method is algebraic, consisting of describing the relative canonical algebra. In the genus 2 case there are classical results of Horikawa that have been used successfully by Xiao Gang to get global results on surfaces. This thesis is mainly concerned with the genus 3 case, which is much harder; even here the results are not definitive. We prove that for genus 2 and 3 the relative canonical algebra is generated in degrees 1, 2, 3 and related in degree ≤ 6. In fact we give a much more detailed analysis of the ring by generators and relations.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Hypersurfaces | ||||
Official Date: | 1988 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Reid, Miles (Miles A.) | ||||
Extent: | 212 leaves | ||||
Language: | eng |
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