This book gives a comprehensive treatment of the singularities that appear in the minimal
model program and in the moduli problem for varieties. The study of these singularities and …

This book is an introduction to singularities for graduate students and researchers. Algebraic
geometry is said to have originated in the seventeenth century with the famous work …

Let $ f:(X, B)\to Z $ be a threefold extremal dlt flipping contraction defined over an
algebraically closed field of characteristic $ p> 5$, such that the coefficients of $\{B\} $ are in …

arXiv:1706.03204v2 [math.AG] 17 Jul 2017 Page 1 arXiv:1706.03204v2 [math.AG] 17 Jul
2017 ON THE RATIONALITY OF KAWAMATA LOG TERMINAL SINGULARITIES IN POSITIVE …

Suppose that X is a projective variety over an algebraically closed field of characteristic p> 0.
Further suppose that L is an ample (or more generally in some sense positive) divisor. We …

We generalize F-signature to pairs (R, D) where D is a Cartier subalgebra on R as defined
by the first two authors. In particular, we show the existence and positivity of the F-signature …

Tight closure test ideals have been central to the classification of singularities in rings of
characteristic $ p> 0$, and via reduction to characteristic $ p> 0$, in equal characteristic 0 as …

We give characterizations of test ideals and $ F $-rational singularities via (regular)
alterations. Formally, the descriptions are analogous to standard characterizations of …

We investigate finite torsors over big opens of spectra of strongly F-regular germs that do not
extend to torsors over the whole spectrum. Let (R,m,k) be a strongly F-regular k-germ where …

We study the behavior of test ideals and F-singularities in families. In particular, we obtain
generic (and non-generic) restriction theorems for test ideals and non-F-pure ideals which …