Discrepancies of $p$-cyclic quotient varieties

Abstract

We consider the quotient variety associated to a linear representation of the cyclic group of order p in characteristic p>0. We estimate the minimal discrepancy of exceptional divisors over the singular locus. In particular, we give criteria for the quotient variety being terminal, canonical and log canonical. As an application, we obtain new examples of non-Cohen-Macaulay terminal singularities, adding to examples recently announced by Totaro.

9 pages v.2: strengthened main results v.3: minor revision

References in corpus (2)

• On the rationality of Kawamata log terminal singularities in positive characteristic
• Rational points on log Fano threefolds over a finite field

Cited by in corpus (1)

• Non-normal purely log terminal centres in characteristic $p\ge 3$