Type: Article

A higher-order tangent map and a conjecture on the higher Nash blowup of curves

Chávez-Martínez, Enrique; Duarte, Daniel; Giles Flores, Arturo;

Abstract:

The authors introduce and investigate a matrix which represents a higher-order tangent map of a morphism. Its definition involves higher-order derivatives, and because of that it is suitable for some computations related to jet spaces. Then they apply the matrix so as to show that the conjecture by Yasuda, concerning the semigroup of the higher Nash blowup of formal curves, holds true for toric curves. Finally, they present a family of non-monomial curves showing that the Yasuda conjecture fails in general.