20 citations · 87 across the 17 of their papers we have counts for
22 papers
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…
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…
Lifting globally -split surfaces to characteristic zero
Fabio Bernasconi, Iacopo Brivio, Tatsuro Kawakami +1
We prove that every globally -split surface admits an equisingular lifting over the ring of Witt vectors.
Relative semiampleness in mixed characteristic
Jakub Witaszek
We show that a nef line bundle on a proper scheme over an excellent base is semiample if and only if it is semiample after restricting to characteristic zero and to positive charac…
The Du Bois complex of a hypersurface and the minimal exponent
Mircea Mustata, Sebastian Olano, Mihnea Popa +1
We study the Du Bois complex of a hypersurface in a smooth complex algebraic variety in terms its minimal exponent . The latter is an in…
Resolution and alteration with ample exceptional divisor
János Kollár, Jakub Witaszek
In this short note we explain how to construct resolutions or regular alterations admitting an ample exceptional divisor, assuming the existence of projective resolutions or regula…
Global Frobenius Liftability II: Surfaces and Fano Threefolds
Piotr Achinger, Jakub Witaszek, Maciej Zdanowicz
In this article, a sequel to "Global Frobenius Liftability I" (math:1708:03777v2), we continue the development of a comprehensive theory of Frobenius liftings modulo . We stud…
Tamely ramified morphisms of curves and Belyi's theorem in positive characteristic
Kiran S. Kedlaya, Daniel Litt, Jakub Witaszek
We show that every smooth projective curve over a finite field k admits a finite tame morphism to the projective line over k. Furthermore, we construct a curve with no such map whe…
On the relative Minimal Model Program for fourfolds in positive and mixed characteristic
Christopher Hacon, Jakub Witaszek
We show the validity of two special cases of the four-dimensional Minimal Model Program in characteristic : for contractions to -factorial fourfolds and in familie…
Keel's base point free theorem and quotients in mixed characteristic
Jakub Witaszek
We develop techniques of mimicking the Frobenius action in the study of universal homeomorphisms in mixed characteristic. As a consequence, we show a mixed characteristic Keel's ba…
The Minimal Model Program for threefolds in characteristic five
Christopher Hacon, Jakub Witaszek
We show the validity of the Minimal Model Program for threefolds in characteristic five.
An analog of adjoint ideals and PLT singularities in mixed characteristic
Linquan Ma, Karl Schwede, Kevin Tucker +2
We use the framework of perfectoid big Cohen-Macaulay algebras to define a class of singularities for pairs in mixed characteristic, which we call purely BCM-regular singularities,…
On the relative Minimal Model Program for threefolds in low characteristics
Christopher Hacon, Jakub Witaszek
We show the validity of the relative dlt MMP over Q-factorial threefolds in all characteristics p>0. As a corollary, we generalise many recent results to low characteristics includ…
On the canonical bundle formula and log abundance in positive characteristic
Jakub Witaszek
We show that a weak version of the canonical bundle formula holds for fibrations of relative dimension one. We provide various applications thereof, for instance, using the recent…
Global Frobenius Liftability I
Piotr Achinger, Jakub Witaszek, Maciej Zdanowicz
We formulate a conjecture characterizing smooth projective varieties in positive characteristic whose Frobenius morphism can be lifted modulo - we expect that such varieties,…
On the rationality of Kawamata log terminal singularities in positive characteristic
Christopher Hacon, Jakub Witaszek
We show that there exists a natural number such that any three-dimensional Kawamata log terminal singularity defined over an algebraically closed field of characteristic $p>p…
On base point free theorem and Mori dream spaces for log canonical threefolds over the algebraic closure of a finite field
Yusuke Nakamura, Jakub Witaszek
The authors and D. Martinelli proved the base point free theorem for big line bundles on a three-dimensional log canonical projective pair defined over the algebraic closure of a f…
Klt del Pezzo surfaces which are not globally F-split
Paolo Cascini, Hiromu Tanaka, Jakub Witaszek
We construct a klt del Pezzo surface which is not globally F-split, over any algebraically closed field of positive characteristic.
On log del Pezzo surfaces in large characteristic
Paolo Cascini, Hiromu Tanaka, Jakub Witaszek
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 lif…
Effective bounds on singular surfaces in positive characteristic
Jakub Witaszek
Using the theory of Frobenius singularities, we show that 13mK_X + 45mA is very ample for an ample Cartier divisor A on a Kawamata log terminal surface X with Gorenstein index m, d…
On base point free theorem for log canonical threefolds over the algebraic closure of a finite field
Diletta Martinelli, Yusuke Nakamura, Jakub Witaszek
We prove the base point free theorem for big line bundles on a three-dimensional log canonical projective pair defined over the algebraic closure of a finite field.
The degeneration of the Grassmannian into a toric variety and the calculation of the eigenspaces of a torus action
Jakub Witaszek
Using the method of degenerating a Grassmannian into a toric variety, we calculate recursive formulas for the dimensions of the eigenspaces of the action of an n-dimensional torus…