arXiv subjects
Publications and source records attributed to Lorenzo Prelli.
Given an ambient variety $X$ and a fixed subvariety $Z$ we give sufficient conditions for the existence of a boundary $Δ$ such that $Z$ is a log canonical center for the pair $(X, Δ)$. We also show that under some additional hypotheses $Δ$ can be chosen such that $(X, Δ)$ has log canonical singularities.
Rational pairs generalize the notion of rational singularities to reduced pairs $(X,D)$. In this paper we deal with the problem of determining whether a normal variety $X$ has a rationalizing divisor, i.e. a reduced divisor $D$ such that $(X, D)$ is a rational pair. We give a criterion for cones to have a rationalizing divisor, and relate the existence of such a divisor to the locus of rational singularities of a variety.