47 citations · 91 across the 15 of their papers we have counts for
17 papers · 1 filter
Abundance for threefolds in positive characteristic
Fabio Bernasconi, Jakub Witaszek, Zheng Xu
We prove the abundance conjecture for threefolds in characteristic .
The Frobenius--stable version of the Grauert--Riemenschneider vanishing theorem fails
Jefferson Baudin, Fabio Bernasconi, Tatsuro Kawakami
We show that the Frobenius--stable version of the Grauert--Riemenschneider vanishing theorem fails for threefolds in any positive characteristic, and for terminal 3-folds in charac…
Counterexamples to the MMP for 1-foliations in positive characteristic
Fabio Bernasconi
We show that many statements of the Minimal Model Program, including the cone theorem, the base point free theorem and the existence of Mori fibre spaces, fail for 1-foliated surfa…
Rational points on 3-folds with nef anti-canonical class over finite fields
Fabio Bernasconi, Stefano Filipazzi
We prove that a geometrically integral smooth 3-fold with nef anti-canonical class and negative Kodaira dimension over a finite field of characteristic and…
Bounding geometrically integral del Pezzo surfaces
Fabio Bernasconi, Gebhard Martin
We prove several boundedness statements for geometrically integral normal del Pezzo surfaces over arbitrary fields. We give an explicit sharp bound on the irregularity if i…
Arithmetic and geometric deformations of 3-folds
Fabio Bernasconi, Iacopo Brivio, Stefano Filipazzi
We show that mixed-characteristic and equi-characteristic small deformations of 3-dimensional canonical (resp. terminal) singularities with perfect residue field of characteristic…
On the properness of the moduli space of stable surfaces over
Emelie Arvidsson, Fabio Bernasconi, Zsolt Patakfalvi
We show the properness of the moduli stack of stable surfaces over , assuming the locally-stable reduction conjecture for stable surfaces. This relies on a local…
Semiampleness for Calabi--Yau surfaces in positive and mixed characteristic
Fabio Bernasconi, Liam Stigant
In this note we prove the semiampleness conjecture for klt Calabi--Yau surface pairs over an excellent base ring. As applications we deduce that generalised abundance and Serrano's…
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.
Abundance theorem for threefolds in mixed characteristic
Fabio Bernasconi, Iacopo Brivio, Liam Stigant
We show the abundance theorem for arithmetic klt threefold pairs whose closed point have residue characteristic greater than five. As a consequence, we give a sufficient condition…
Vanishing theorems for threefolds in characteristic
Fabio Bernasconi, János Kollár
We prove Grauert-Riemenschneider-type vanishing theorems for excellent dlt threefolds pairs whose closed points have perfect residue fields of positive characteristic . Then w…
A vanishing theorem for threefolds in characteristic and applications
Fabio Bernasconi
In this note we show a Kawamata-Viehweg vanishing theorem for pl-contractions on threefolds in characteristic . We deduce several applications for klt threefolds: the vanishin…
On the Kawamata-Viehweg vanishing theorem for log del Pezzo surfaces in positive characteristic
Emelie Arvidsson, Fabio Bernasconi, Justin Lacini
We prove the Kawamata-Viehweg vanishing theorem for surfaces of del Pezzo type over perfect fields of positive characteristic . As a consequence, we show that klt threefold si…
On the base point free theorem for klt threefolds in large characteristic
Fabio Bernasconi
In this article we present a refinement of the base point free theorem for threefolds in positive characteristic. If is a nef Cartier divisor of numerical dimension at least on…
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…
Non-normal purely log terminal centres in characteristic
Fabio Bernasconi
In this note we show, building on a recent work of Totaro, that for every prime number there exists a purely log terminal pair of dimension whose plt cent…
Kawamata-Viehweg vanishing fails for log del Pezzo surfaces in characteristic 3
Fabio Bernasconi
We construct a klt del Pezzo surface in characteristic three violating the Kawamata-Viehweg vanishing theorem. As a consequence we show that there exists a Kawamata log terminal th…