近年,Du Bois特異点の高次版である高次Du Bois特異点が盛んに研究されている.本講義では,その正標数アナログである高次F単射特異点について紹介する.時間が余れば,高次F有理特異点とその正標数アナログについても解説する.
In recent years, higher Du Bois singularities, which can be regarded as a `higher' version of Du Bois singularities, have been actively studied. In this lecture, I will introduce higher F-injective singularities, which are their positive characteristic analogs. If time permits, I will also discuss higher F-rational singularities and their positive characteristic analogs.