We decompose the Jacobian variety of hyperelliptic curves up to genus 10, defined over an algebraically closed field of characteristic zero, with reduced automorphism group A 4 , S 4 , or A 5 .
creator
Paulhus, Jennifer (Faculty/Staff)
Title
Elliptic Factors in Jacobians of Hyperelliptic Curves with Certain Automorphism Groups
supporting host
Grinnell College. Mathematics and Statistics
Index Date
2008
Date Issued
41592
Date (Other)
31-Aug-2008
Publisher
Grinnell College
Genre
Essays
Digital Origin
born digital
Extent
17 pages
Media Type
application/pdf
citation/reference
Paulhus, Jennifer. 2013. Elliptic factors in Jacobians of hyperelliptic curves with certain automorphism groups. in ANTS X. Berkeley, CA: Mathematical Science Publishers.p. 487-505. DOI: 10.2140/obs.2013.1.487
description
We decompose the Jacobian variety of hyperelliptic curves up to genus 10, defined over an algebraically closed field of characteristic zero, with reduced automorphism group A 4 , S 4 , or A 5 . Among those curves is a genus 4 curve with Jacobian variety isogenous to E 2 1 +? E 2 2 and a genus 5 curve with Jacobian variety isogenous to E 5 for E and E i elliptic curves. These types of results have some interesting consequences to questions of ranks of elliptic curves and ranks of their twists.
Language
English
Topic
Jacobians
Topic
Elliptic functions
Topic
Reimann surfaces
Temporal
21st century
Keyword
automorphism groups of Riemann surfaces
Keyword
Jacobian varieties
Keyword
hyperelliptic curves
Classification
QA
Related Item
Faculty Scholarship
Related Item
Scholarship at Grinnell
Related Item
Digital Grinnell
Identifier (hdl)
http://hdl.handle.net/11084/3326
Identifier (local)
grinnell:3326
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.).
