HIGHER NASH BLOW-UPS AND NOBILE’S THEOREM

Abstract

The dissertation talks about the study the higher Nash blow-ups introduced by T.~Yasuda, an approach towards resolution of singularities. The important step towards the resolution problem is the higher Nobile’s theorem. We investigate this theorem for the graded case and the 2nd order Nash blow-ups. We see a possible idea that connects the graded case to the general case. Finally, we show a special case of the (higher) Zariski-Lipman conjecture and how it relates to the (higher) Nobile's theorem.