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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