# Jet schemes of homogeneous hypersurfaces

• ### Shihoko Ishii

University of Tokyo, Japan
• ### Akiyoshi Sannai

Nagoya University, Japan
• ### Kei-ichi Watanabe

College of Humanities and Sciences, Tokyo, Japan

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## Abstract

This paper studies the singularities of jet schemes of homogeneous hypersurfaces of general type. We obtain the condition of the degree and the dimension for the singularities of the jet schemes to be of dense $F$-regular type. This provides us with examples of singular varieties whose $m$-jet schemes have rational singularities for every $m$.