8 papers
Liftability and vanishing theorems for Fano threefolds in positive characteristic I
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…
Mumford vanishing for threefolds in positive characteristic
Tatsuro Kawakami, Hiromu Tanaka
Let be a projective klt threefold in characteristic and let be a nef Cartier divisor on . We show that for the following two cases: (1) is not…
Prime Fano threefolds of genus 8 in positive characteristic
Akihiro Kanemitsu, Hiromu Tanaka
We prove that a prime Fano threefold of genus 8 over an algebraically closed field of positive characteristic is isomorphic to a linear section of the Grassmannian variety Gr(2, 6)…
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.
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…
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…