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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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Schottky algorithms: Classical meets tropical
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by Lynn Chua, Mario Kummer and Bernd Sturmfels HTML | PDF
Math. Comp. 88 (2019), 2541-2558 Request permission

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.
  • © Copyright 2018 American Mathematical Society
  • Journal: Math. Comp. 88 (2019), 2541-2558
  • MSC (2010): Primary 14H42, 14T05; Secondary 51M10, 14A40
  • DOI: https://doi.org/10.1090/mcom/3406
  • MathSciNet review: 3957905