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Mathematics of Computation

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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
MathSciNet review: 3957905
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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.


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Additional Information

Lynn Chua
Affiliation: Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, California 94720
MR Author ID: 1037521
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
MR Author ID: 238151
Email: bernd@mis.mpg.edu, bernd@berkeley.edu

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