Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Schottky algorithms: Classical meets tropical


Authors: Lynn Chua, Mario Kummer and Bernd Sturmfels
Journal: Math. Comp. 88 (2019), 2541-2558
MSC (2010): Primary 14H42, 14T05; Secondary 51M10, 14A40
DOI: https://doi.org/10.1090/mcom/3406
Published electronically: December 27, 2018
Full-text PDF
View in AMS MathViewer New

Abstract | References | Similar Articles | Additional Information

Abstract: We present a new perspective on the Schottky problem that links numerical computing with tropical geometry. The task is to decide whether a symmetric matrix defines a Jacobian, and, if so, to compute the curve and its canonical embedding. We offer solutions and their implementations in genus four, both classically and tropically. The locus of cographic matroids arises from tropicalizing the Schottky-Igusa modular form.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 14H42, 14T05, 51M10, 14A40

Retrieve articles in all journals with MSC (2010): 14H42, 14T05, 51M10, 14A40


Additional Information

Lynn Chua
Affiliation: Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, California 94720
Email: chualynn@berkeley.edu

Mario Kummer
Affiliation: Institut für Mathematik, Technische Universität Berlin, D-10623 Berlin, Germany
Email: kummer@tu-berlin.de

Bernd Sturmfels
Affiliation: Max Planck Institute for Mathematics in the Sciences, D-04103 Leipzig, Germany; and Department of Mathematics, University of California, Berkeley, Berkeley, California 94720
Email: bernd@mis.mpg.edu, bernd@berkeley.edu

DOI: https://doi.org/10.1090/mcom/3406
Received by editor(s): July 26, 2017
Received by editor(s) in revised form: September 30, 2018
Published electronically: December 27, 2018
Additional Notes: The first author was supported by a UC Berkeley University Fellowship and the Max Planck Institute for Mathematics in the Sciences, Leipzig.
The third author received funding from the US National Science Foundation (DMS-1419018) and the Einstein Foundation Berlin.
Article copyright: © Copyright 2018 American Mathematical Society