On rationalizing divisors
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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.
KeywordsSingularities Rational pairs Divisors
The author would like to thank his advisor Sándor Kovács for his supervision, direction, and many insights into the subject of this project. The author would also like to thank Siddharth Mathur for numerous useful conversations.
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