Rational Formulas for Traces in zero-dimensional Algebras
Carlos D'Andrea, Gabriela Jeronimo
Abstract
We present a rational expression for the trace of the multiplication map Mr in a finite-dimensional algebra of the form A:=K[x1,...,xn]/I in terms of the generalized Chow form of I. Here, I is a zero-dimensional ideal of K[x1,...,xn] is a zero-dimensional ideal, K is a field of characteristic zero, and r(x1,..., xn) a rational function whose denominator is not a zero divisor in A. If I is a complete intersection in the torus, we get numerator and denominator formulas for traces in terms of sparse resultants.
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