Tropicalization and irreducibility of generalized Vandermonde determinants

D’Andrea, Carlos; Tabera, Luis

doi:10.1090/S0002-9939-09-09951-1

Tropicalization and irreducibility of generalized Vandermonde determinants
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by Carlos D’Andrea and Luis Felipe Tabera PDF

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

Abstract:

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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