Zobrazeno 1 - 10
of 59
pro vyhledávání: '"Bernasconi, Fabio"'
Autor:
Bernasconi, Fabio, Tanaka, Hiromu
We classify geometrically integral regular del Pezzo surfaces which are not geometrically normal over imperfect fields of positive characteristic. Based on this classification, we show that a three-dimensional terminal del Pezzo fibration onto a curv
Externí odkaz:
http://arxiv.org/abs/2408.11378
For every $d \geq 4$, we construct a $d$-dimensional, log canonical, $K$-trivial variety with the property that two general fibers of its Albanese morphism are not birational. This provides a strong counterexample to the Beauville--Bogomolov decompos
Externí odkaz:
http://arxiv.org/abs/2407.17260
We prove the Sarkisov program for projective surfaces over excellent base rings, including the case of non-perfect base fields of characteristic p>0. We classify the Sarkisov links between Mori fibre spaces and their relations for regular surfaces, g
Externí odkaz:
http://arxiv.org/abs/2404.03281
We show that the Frobenius--stable version of the Grauert--Riemenschneider vanishing theorem fails for terminal 3-folds in characteristic $p \in \left\{2, 3, 5\right\}$. To prove this, we introduce the notion of $\mathbb{F}_p$-rationality for singula
Externí odkaz:
http://arxiv.org/abs/2312.13456
Autor:
Bernasconi, Fabio
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 surface pairs $(X,\mathcal{F})$ with canonical singularities in characteris
Externí odkaz:
http://arxiv.org/abs/2309.13978
Autor:
Bernasconi, Fabio, Filipazzi, Stefano
We prove that a geometrically integral smooth 3-fold $X$ with nef anti-canonical class and negative Kodaira dimension over a finite field $\mathbb{F}_q$ of characteristic $p>5$ and cardinality $q=p^e > 19$ has a rational point. Additionally, under th
Externí odkaz:
http://arxiv.org/abs/2308.10824
Autor:
Bernasconi, Fabio, Martin, Gebhard
We prove several boundedness statements for geometrically integral normal del Pezzo surfaces $X$ over arbitrary fields. We give an explicit sharp bound on the irregularity if $X$ is canonical or regular. In particular, we show that wild canonical del
Externí odkaz:
http://arxiv.org/abs/2306.07000
Publikováno v:
Bull. Lond. Math. Soc. 56 (2024), no. 1, 423-443
We show that mixed-characteristic and equi-characteristic small deformations of 3-dimensional canonical (resp. terminal) singularities with perfect residue field of characteristic $p>5$ are canonical (resp. terminal). We discuss applications to arith
Externí odkaz:
http://arxiv.org/abs/2303.06036
We show the properness of the moduli stack of stable surfaces over $\mathbb{Z}[1/30]$, assuming the locally-stable reduction conjecture for stable surfaces. This relies on a local Kawamata--Viehweg vanishing theorem for for 3-dimensional log canonica
Externí odkaz:
http://arxiv.org/abs/2302.05651
Autor:
Bernasconi, Fabio, Stigant, Liam
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 conjecture hold for surfaces. Finally, we study the semiampleness con
Externí odkaz:
http://arxiv.org/abs/2207.03002