Research

Research Interests

My area of research is Algebraic Geometry. I mainly work on the following topics:

• Higher Nash Blow-ups

• Module of Principal Parts

• Determinantal Varieties

• Higher Zariski-Lipman Conjecture (Hypersurface case, Graded case)

Preprints

• Higher Nash Blow-ups and Nobile's Theorem [arXiv] (submitted)

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.

In Preparation

• Higher Zariski-Lipman Conjecture for Homogeneous Hypersurfaces  (Joint with Claudia Miller)

We prove the higher Zariski-Lipman conjecture for hypersurfaces given by homogeneous equations over a field of characteristic zero.