Higher Nash blow-ups and Nobile theorem

TL;DR

This paper explores higher Nash blow-ups and extends Nobile's theorem to these cases, providing characteristic-free proofs for graded cases and specific second-order cases in characteristic zero.

Contribution

It offers the first characteristic-free proof of the higher Nobile's theorem for graded cases and addresses second-order Nash blow-ups in characteristic zero.

Findings

Established a characteristic-free proof for the higher Nobile's theorem in graded cases.

Provided a proof for second-order Nash blow-ups in characteristic zero.

Extended classical results to higher Nash blow-ups in algebraic geometry.

Abstract

We study the higher Nash blow-ups introduced by T. Yasuda and investigate the higher version of the classical Nobile's theorem. In particular, we give a characteristic free proof of the higher Nobile's theorem for the graded case. We also give a proof for the 2nd order Nash blow-ups in characteristic zero.