Tropicalization and irreducibility of Generalized Vandermonde Determinants

Details Tropicalization and irreducibility of Generalized Vandermonde Determinants Tropicalization and irreducibility of Generalized Vandermonde Determinants

2008-03-14

arxiv.org/abs/0803.2166v2

Proc. Amer. Math. Soc. 137 (2009), 3647-3656

Mathematics

Commutative Algebra

10 pages, AMSart. Revised version to appear in Proceedings of the AMS

Scientific paper

10.1090/S0002-9939-09-09951-1

We find geometric and arithmetic conditions in order to characterize the
irreducibility of the determinant of the generic Vandermonde matrix over the
algebraic closure of any field k. We also characterize those determinants whose
tropicalization with respect to the variables of a row is irreducible.

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