Tropicalization and Irreducibility of Generalized Vandermonde Determinants
نویسندگان
چکیده
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.
منابع مشابه
On the Irreducibility of Generalized Vandermonde Determinants
We find geometric and arithmetic conditions on a finite set of integer exponents and the characteristic of a field k in order to characterize the irreducibility of the determinant of the generic Vandermonde matrix determined by these exponents in the algebraic closure of k. Tools from Tropical Geometry are then applied in order to characterize those determinants that are irreducible over any fi...
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