1 citations · 1 across the 12 of their papers we have counts for
13 papers
Frobenius splitting for Fano threefolds
Hiromu Tanaka
We prove that every smooth Fano threefold of characteristic p>5 is quasi-F-split. Moreover, if p>11, then it is F-split.
105 families of Fano threefolds in positive characteristic
Hiromu Tanaka
Over an algebraically closed field of characteristic , we prove that smooth Fano threefolds form 105 irreducible deformation families.
Prime Fano threefolds in positive characteristic
Akihiro Kanemitsu, Hiromu Tanaka
We prove that every prime Fano threefold of genus in positive characteristic is a linear section of a Mukai variety.
Mukai bundles and Brill-Noether generality for prime Fano threefolds in positive characteristic
Hiromu Tanaka
Let be a prime Fano threefold of genus in positive characteristic. For every nontrivial decomposition , we prove that there exists a unique Mukai bundle on …
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)…
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…
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…