## Tropical discriminants

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- by Alicia Dickenstein, Eva Maria Feichtner and Bernd Sturmfels
- J. Amer. Math. Soc.
**20**(2007), 1111-1133 - DOI: https://doi.org/10.1090/S0894-0347-07-00562-0
- Published electronically: April 23, 2007
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## 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.## References

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## Bibliographic 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. - © 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

Dedicated: Dedicated to the memory of Pilar Pisón Casares