We present a new technique to study Jacobian variety decompositions using subgroups of the automorphism group of the curve and the corresponding intermediate covers.
creator
Paulhus, Jennifer (Faculty/Staff)
creator
Rojas, Anita M.
Title
Completely Decomposable Jacobian Varieties in New Genera
supporting host
Grinnell College. Mathematics & Statistics
Index Date
2016
Date Issued
08-Jun-2016
Publisher
Grinnell College
Genre
Essays
Digital Origin
born digital
Extent
21 pages
Media Type
application/pdf
description
We present a new technique to study Jacobian variety decompositions using subgroups of the automorphism group of the curve and the corresponding intermediate covers. In particular, this new method allows us to produce many new examples of genera for which there is a curve with completely decomposable Jacobian. These examples greatly extend the list given by Ekedahl and Serre of genera containing such curves, and provide more evidence for a positive answer to two questions they asked. Additionally, we produce new examples of families of curves, all of which have completely decomposable Jacobian varieties. These families relate to questions about special subvarieties in the moduli space of principally polarized abelian varieties.
citation
Paulhus, Jennifer, and Anita M. Rojas. "Completely decomposable Jacobian varieties in new genera." Experimental Mathematics 26.4 (2017): 430-445. ~ citation
Language
English
Topic
Decomposition (Mathematics)
Topic
Jacobians
Keyword
Jacobian Varieties
Keyword
Group Algebra Decomposition
Keyword
Completely Decomposable
Classification
QA
Related Item
Faculty Scholarship
Related Item
Scholarship at Grinnell
Related Item
Digital Grinnell
Identifier (hdl)
http://hdl.handle.net/11084/13253
Identifier (local)
grinnell:13253
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.).