We present a decomposition of the Jacobian varieties for all curves of this type and prove that no such Jacobian variety is simple.
creator
Fischer, Allison (Class of 2015)
creator
Liu, Mouchen (Class of 2015)
creator
Paulhus, Jennifer (Faculty/Staff)
Title
Jacobian Varieties of Hurwitz Curves with Automorphism Group PSL(2,q)
supporting host
Grinnell College. Mathematics & Statistics
Index Date
2015
Date Issued
22-Jul-2015
Publisher
Grinnell College
Genre
Essays
Digital Origin
born digital
Extent
20 pages
Media Type
application/pdf
description
The size of the automorphism group of a compact Riemann surface of genus g > 1 is bounded by 84(g-1). Curves with automorphism group of size this bound are called Hurwitz curves. In many cases the automorphism group of these curves is the projective special linear group PSL(2,q). We present a decomposition of the Jacobian varieties for all curves of this type and prove that no such Jacobian variety is simple.
citation
Fischer, Allison, Mouchen Liu, and Jennifer Paulhus. "Jacobian varieties of Hurwitz curves with automorphism group PSL (2, q)." Involve, a Journal of Mathematics 9.4 (2016): 639-655. ~ citation
Language
English
Topic
Jacobians
Topic
Curves, Algebraic
Keyword
Representation theory
Keyword
Jacobian Varieties
Keyword
Hurwitz curves
Keyword
Projective special linear group
Classification
QA
Related Item
Mentored Advanced Project
Related Item
Faculty Scholarship
Related Item
Student Scholarship
Related Item
Scholarship at Grinnell
Related Item
Digital Grinnell
Identifier (hdl)
http://hdl.handle.net/11084/13254
Identifier (local)
grinnell:13254
Access Condition
Copyright to this work is held by the author(s), in accordance with United States copyright law (USC 17). Readers of this work have certain rights as defined by the law, including but not limited to fair use (17 USC 107 et seq.).
