Rational singularities.

By S'andor J. Kov'acs. 2017

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A resolution-free definition of rational singularities is introduced, and it is proved that for a variety admitting a resolution of singularities, this is equivalent to the usual definition. It is also demonstrated that rational singularities are equivalent to pseudo-rational singularities. As applications, several open questions about the higher direct images of structure sheaves and dualizing sheaves are answered and it is proved that Cohen-Macaulay klt singularities are rational in arbitrary characteristic.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f9f07803905e396a95245d85c4977ca27b12594c