Lopes, Margarida Mendes (1988) The relative canonical algebra for genus 3 fibrations. PhD thesis, University of Warwick.

Preview

PDF WRAP_Theses_Lopes_1988.pdf - Submitted Version - Requires a PDF viewer. Download (4Mb) | Preview

Request Changes to record.

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)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Hypersurfaces
Official Date:	1988
Dates:	Date Event 1988 Submitted
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Publication Status:	Unpublished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

Request changes or add full text files to a record

Repository staff actions (login required)

View Item

Downloads