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Geometry and arithmetic of geometrically integral regular del Pezzo surfaces
Fabio Bernasconi, Hiromu Tanaka
We classify geometrically integral regular del Pezzo surfaces which are not geometrically normal over imperfect fields of positive characteristic. Based on this classification, we…
Quasi-F-splittings in birational geometry III
Tatsuro Kawakami, Teppei Takamatsu, Hiromu Tanaka +3
We prove that -Gorenstein quasi--regular singularities are klt. To this end, we shall introduce quasi-test ideals.
Weak quasi--splitting and del Pezzo varieties
Tatsuro Kawakami, Hiromu Tanaka
We show that smooth del Pezzo varieties in positive characteristic are quasi--split. To this end, we introduce weak quasi--splitting and we prove that general ladders of smoo…
Quasi--splittings and quasi--regularity
Hiromu Tanaka, Jakub Witaszek, Fuetaro Yobuko
We develop the theory of quasi--splittings, quasi--regularity, and quasi--regularity.
Global -regularity for weak del Pezzo surfaces
Tatsuro Kawakami, Hiromu Tanaka
Let be an algebraically closed field of characteristic . Let be a normal projective surface over with canonical singularities whose anti-canonical divisor is nef a…
Liftability and vanishing theorems for Fano threefolds in positive characteristic II
Tatsuro Kawakami, Hiromu Tanaka
In our series of papers, we prove that smooth Fano threefolds in positive characteristic lift to the ring of Witt vectors. Moreover, we show that they satisfy Akizuki-Nakano vanish…