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Torsion-free rank one sheaves on a semi-stable curve

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Torsion-free rank one sheaves on a semi-stable curve

Orecchia, Giulio (2014) Torsion-free rank one sheaves on a semi-stable curve. Masters thesis, Concordia University.

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Abstract

The aim of this work is to build a compactification of the Picard scheme for a particular reducible semi-stable curve of genus 1 over a field k. The curve X is given by two copies of the projective line intersecting at two nodes. The compactification is given by the moduli space of torsion-free rank one sheaves on X. We give an alternative definition of such sheaves on the base change of X to any k-scheme S. Then we prove that the stack of rigidified, simple torsion-free rank one sheaves is a scheme, covered by copies of the original curve X.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Orecchia, Giulio
Institution:Concordia University
Degree Name:M. Sc.
Program:Mathematics
Date:9 July 2014
Thesis Supervisor(s):Edixhoven, Sebastiaan Johan
Keywords:Torsion-free sheaves, Picard scheme, compactification
ID Code:978897
Deposited By: GIULIO ORECCHIA
Deposited On:11 Nov 2014 15:32
Last Modified:18 Jan 2018 17:47

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