On the anti-canonical ring and varieties of Fano type

We study the anti-canonical ring of a projective variety and we characterise varieties of log Fano type depending on the singularities of these models.Comment: 13 pages, v2: remove Example 5.2 from v1, v3: Reference adde

New outlook on the minimal model program, I

We give a new and self-contained proof of the finite generation of adjoint rings with big boundaries. As a consequence, we show that the canonical ring of a smooth projective variety is finitely generated.Comment: to appear in Duke Math.

On log del Pezzo surfaces in large characteristic

We show that any Kawamata log terminal del Pezzo surface over an algebraically closed field of large characteristic is globally F-regular or it admits a log resolution which is liftable to characteristic zero. As a consequence, we prove the Kawamata-Viehweg vanishing theorem for klt del Pezzo surfaces of large characteristic.Comment: v2: final version. To appear in Compositio Mathematic

A remark on the Ueno-Campana's threefold

We show that the Ueno-Campana's threefold cannot be obtained as the blow-up of any smooth threefold along a smooth centre, answering negatively a question raised by Oguiso and Truong.Comment: To appear on Michigan Math. Journal, Vol. 65 (2016