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Tropical discriminants
Author(s):
Alicia
Dickenstein;
Eva
Maria
Feichtner;
Bernd
Sturmfels
Journal:
J. Amer. Math. Soc.
20
(2007),
1111-1133.
MSC (2000):
Primary 14M25;
Secondary 52B20
Posted:
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  -discriminant is the tropicalization of the dual variety of the projective toric variety given by an integer matrix  . This tropical algebraic variety is shown to coincide with the Minkowski sum of the row space of  and the tropicalization of the kernel of  . This leads to an explicit positive formula for all the extreme monomials of any  -discriminant.
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Additional Information:
Alicia
Dickenstein
Affiliation:
Departamento de Matemática, FCEN, Universidad de Buenos Aires, (1428) B. Aires, Argentina
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
Email:
bernd@math.berkeley.edu
DOI:
10.1090/S0894-0347-07-00562-0
PII:
S 0894-0347(07)00562-0
Keywords:
Tropical geometry,
dual variety,
discriminant.
Received by editor(s):
November 8, 2005
Posted:
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 of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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