Login | Register

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


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.

Text (application/pdf)
Orecchia_MSc_F2014.pdf - Accepted Version


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.
Date:9 July 2014
Thesis Supervisor(s):Edixhoven, Sebastiaan Johan
Keywords:Torsion-free sheaves, Picard scheme, compactification
ID Code:978897
Deposited On:11 Nov 2014 15:32
Last Modified:18 Jan 2018 17:47


[1] Brian Conrad, Grothendieck duality and base change
Lecture Notes in Mathematics, vol. 1750, Springer-Verlag, Berlin, 2000.
[2] Eduardo Esteves, Compactifying the relative Jacobian over families of reduced
Transactions of the American Mathematical Society, Volume 353, Number 8, pag.
[3] Daniel Ferrand, Conducteur, descente et pincement
Bull. Soc. math. France, 131 (4), 2003, p.553-585.
[4] Alexander Grothendieck and Jean Dieudonné, EGA IV, Étude locale de schémas
et des morphismes de schémas
Ibid. 20 (1964), 24(1965), 28(1966), 32(1967).
[5] Sean Howe, Higher genus counterexamples to relative Manin-Mumford
Master thesis, 2012.
[6] David Mumford, Abelian varieties
Oxford University Press, 1970.
[7] David Mumford, John Fogarty, Frances Clare Kirwan Geometric invariant theory
3rd edition, Ergebnisse Math. 34, Springer-Verlag, Berlin, 1994.
[8] Nicholas M. Katz, Barry Mazur, Arithmetic Moduli of Elliptic Curves
Princeton University Press, 1985.
[9] Gérard Laumon, Laurent Moret-Bailly, Champs algébriques
Ergeb. Math. Grenzgeb. (3), Volume 39, Springer ,1999.
[10] Qing Liu, Algebraic geometry and arithmetic curves
Oxford Graduate Texts in Mathematics, 2002.
[11] The Stacks Project
All items in Spectrum are protected by copyright, with all rights reserved. The use of items is governed by Spectrum's terms of access.

Repository Staff Only: item control page

Downloads per month over past year

Back to top Back to top