Rational singularities
Abstract
A resolution-free definition of rational singularities is introduced, and it is proved that for a variety admitting a resolution of singularities, so in particular in characteristic zero, this is equivalent to the usual definition. It is also demonstrated that pseudo-rational singularities are rational. The main theorem, a Kempf-type criterion for rational singularities, is new even in characteristic zero contrasting an earlier result of Cutkosky that a similar result with slightly different assumptions could not hold. Several applications are included. In particular, an Elkik-type theorem, proving that Cohen-Macaulay dlt singularities are rational in arbitrary characteristic.
Keywords
Cite
@article{arxiv.1703.02269,
title = {Rational singularities},
author = {Sándor J Kovács},
journal= {arXiv preprint arXiv:1703.02269},
year = {2024}
}
Comments
There's likely an error in the proof of the main theorem. Many intermediate results are correct and will be included elsewhere. The main result may be correct under stronger assumptions