30 citations · 200 across the 41 of their papers we have counts for
43 papers
Fano threefolds in positive characteristic IV
Hiromu Tanaka
Based on the former parts, we classify smooth Fano threefolds of positive characteristic.
Fano threefolds in positive characteristic III
Masaya Asai, Hiromu Tanaka
We classify primitive Fano threefolds in positive characteristic whose Picard numbers are at least two. We also classify Fano theefolds of Picard rank two.
Fano threefolds in positive characteristic II
Hiromu Tanaka
Let be a smooth Fano threefold over an algebraically closed field of positive characteristic. Assume that is very ample and each of the index and the Picard number is…
Fano threefolds in positive characteristic I
Hiromu Tanaka
Over an algebraically closed field of positive characteristic, we classify smooth Fano threefolds of Picard number one whose anti-canonical linear systems are not very ample. Furth…
Discriminant divisors for conic bundles
Hiromu Tanaka
We study some foundational properties on discriminant divisors for generically smooth conic bundles. In particular, we extend the formula to arbitrary ch…
Elliptic singularities and threefold flops in positive characteristic
Hiromu Tanaka
Let be a smooth threefold over an algebraically closed field of positive characteristic. We prove that an arbitrary flop of is smooth. To this end, we study Gorenstein curv…
Quasi-F-splittings in birational geometry II
Tatsuro Kawakami, Teppei Takamatsu, Hiromu Tanaka +3
Over an algebraically closed field of characteristic , we prove that three-dimensional -factorial affine klt varieties are quasi--split. Furthermore, we show th…
Kawamata-Viehweg vanishing for toric varieties
Hiromu Tanaka
Given a boundary divisor on a projective toric variety such that is klt, we establish the Kawamata-Viehweg vanishing theorem for .
Quasi-F-splittings in birational geometry
Tatsuro Kawakami, Teppei Takamatsu, Hiromu Tanaka +3
We develop the theory of quasi--splittings in the context of birational geometry. Amongst other things, we obtain results on liftability of sections and establish a criterion fo…
Contraction images of toric varieties
Hiromu Tanaka
Let be a proper morphism of normal varieties with . If is toric, then is toric and is a toric morphism for some toric stru…
Bertini theorems admitting base changes
Hiromu Tanaka
Given a base point free linear system on an algebraic variety, many classes of singularities are stable under taking suitable members after enlarging the base field. We establish a…
On p-power freeness in positive characteristic
Hiromu Tanaka
In this note, we study base point freeness up to taking p-power, which we will call p-power freeness. We first establish some criteria for p-power freeness as analogues of criteria…
Boundedness of regular del Pezzo surfaces over imperfect fields
Hiromu Tanaka
For a regular del Pezzo surface , we prove that is very ample. Furthermore, we also give an explicit upper bound for the volume which depends only on $[k : k^…
On del Pezzo fibrations in positive characteristic
Fabio Bernasconi, Hiromu Tanaka
We establish two results on three-dimensional del Pezzo fibrations in positive characteristic. First, we give an explicit bound for torsion index of relatively torsion line bundles…
Invariants of algebraic varieties over imperfect fields
Hiromu Tanaka
We introduce four invariants of algebraic varieties over imperfect fields, each of which measures either geometric non-normality or geometric non-reducedness. The first objective o…
A Witt Nadel vanishing theorem for threefolds
Yusuke Nakamura, Hiromu Tanaka
In this paper, we establish a vanishing theorem of Nadel type for the Witt multiplier ideals on threefolds over perfect fields of characteristic larger than five. As an application…
Minimal model program for log canonical threefolds in positive characteristic
Kenta Hashizume, Yusuke Nakamura, Hiromu Tanaka
Given a three-dimensional projective log canonical pair over a perfect field of characteristic larger than five, there exists a minimal model program that terminates after finitely…
Zariskian adic spaces
Hiromu Tanaka
We introduce a Zariskian analogue of the theory of Huber's adic spaces.
Vanishing theorems of Kodaira type for Witt canonical sheaves
Hiromu Tanaka
Given a smooth projective variety over a perfect field of positive characteristic, we prove that the higher cohomologies vanish for the tensor product of the Witt canonical sheaf a…
Relative semi-ampleness in positive characteristic
Paolo Cascini, Hiromu Tanaka
Given an invertible sheaf on a fibre space between projective varieties of positive characteristic, we show that fibrewise semi-ampleness implies relative semi-ampleness. The same…
Infinite dimensional excellent rings
Hiromu Tanaka
In this note, we prove that there exist infinite dimensional excellent rings.
Infinitely generated symbolic Rees algebras over finite fields
Akiyoshi Sannai, Hiromu Tanaka
For the polynomial ring over an arbitrary field with twelve variables, there exists a prime ideal whose symbolic Rees algebra is not finitely generated.
A characterization of ordinary abelian varieties by the Frobenius push-forward of the structure sheaf II
Sho Ejiri, Akiyoshi Sannai
In this paper, we prove that a smooth projective variety of characteristic is an ordinary abelian variety if and only if is pseudo-effective and …
Pathologies on Mori fibre spaces in positive characteristic
Hiromu Tanaka
We show that there exist Mori fibre spaces whose total spaces are klt but bases are not. We also construct Mori fibre spaces which have relatively non-trivial torsion line bundles.