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Dias, Eduardo Manuel (2016) Algebraic covers. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b2876030~S1
Abstract
The main goal of this thesis is the description of the section ring of a surface R(S,L) = O∞n=0 H0(S,nL) where L is an ample base point free divisor defining a covering map φL: S -> P2 such that φ*OS = OP2 O
Ω1P2 O Ω1P2 O Op2(-3). This is an abelian surface with a polarization of type (1,3) which was studied before in [BL94, Cas99, Cas12].
Given a covering map φ: X -> Y, following the methods introduced by Miranda for general d covers, in chapter 3 we will define a cover homomorphism that will induce a commutative and associative multiplication in φ*OX.
Chapter 4 focuses in the OP2-modules Hom (S2Ω1P2,Ω1P2) that will be used to define a commutative multiplication for our surface. Chapter 5 is about the associative condition. It is a computational method based on the paper [Rei90].
In the last chapter we use the ring R(S,L) to prove that the moduli space of abelian surfaces with a polarization of type (1,3) and canonical level structure is rational. We will also show how to use the same method to find models for covering maps such that φ*OS = OP2 O Ω1P2(-m1) O Ω1P2(-m2) O OP2(-m1-m2-3).
The last section contains new problems whose goal is to construct and study algebraic varieties given by the vanishing of a high codimensional Gorenstein ideal.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Mappings (Mathematics), Rings (Algebra), Surfaces | ||||
Official Date: | February 2016 | ||||
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Publication Status: | Unpublished | ||||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.) | ||||
Sponsors: | Fundação para a Ciência e a Tecnologia (FCT) [SFRH/BD/61216/2009] | ||||
Extent: | vii, 86 leaves | ||||
Language: | eng |
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