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Journal of the American Mathematical Society

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

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Tropical discriminants
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by Alicia Dickenstein, Eva Maria Feichtner and Bernd Sturmfels PDF
J. Amer. Math. Soc. 20 (2007), 1111-1133 Request permission

Abstract:

Tropical geometry is used to develop a new approach to the theory of discriminants and resultants in the sense of Gel$’$fand, Kapranov and Zelevinsky. The tropical $A$-discriminant is the tropicalization of the dual variety of the projective toric variety given by an integer matrix $A$. This tropical algebraic variety is shown to coincide with the Minkowski sum of the row space of $A$ and the tropicalization of the kernel of $A$. This leads to an explicit positive formula for all the extreme monomials of any $A$-discriminant.
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Additional Information
  • Alicia Dickenstein
  • Affiliation: Departamento de Matemática, FCEN, Universidad de Buenos Aires, (1428) B. Aires, Argentina
  • MR Author ID: 57755
  • Email: alidick@dm.uba.ar
  • Eva Maria Feichtner
  • Affiliation: Department of Mathematics, ETH Zürich, 8092 Zürich, Switzerland
  • Address at time of publication: Department of Mathematics, University of Stuttgart, 70569 Stuttgart, Germany
  • Email: feichtne@igt.uni-stuttgart.de
  • Bernd Sturmfels
  • Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
  • MR Author ID: 238151
  • Email: bernd@math.berkeley.edu
  • Received by editor(s): November 8, 2005
  • Published electronically: April 23, 2007
  • Additional Notes: The first author was partially supported by UBACYT X042, CONICET PIP 5617 and ANPCYT 17-20569, Argentina.
    The second author was supported by a Research Professorship of the Swiss National Science Foundation, PP002–106403/1.
    The last author was partially supported by the U.S. National Science Foundation, DMS-0456960.

  • Dedicated: Dedicated to the memory of Pilar Pisón Casares
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 20 (2007), 1111-1133
  • MSC (2000): Primary 14M25; Secondary 52B20
  • DOI: https://doi.org/10.1090/S0894-0347-07-00562-0
  • MathSciNet review: 2328718