# Vanishing theorems for threefolds in characteristic $p>5$.

@article{Bernasconi2020VanishingTF, title={Vanishing theorems for threefolds in characteristic \$p>5\$.}, author={F. Bernasconi and J. Koll'ar}, journal={arXiv: Algebraic Geometry}, year={2020} }

We prove Grauert-Riemenschneider-type vanishing theorems for excellent dlt threefolds pairs whose closed points have perfect residue fields of characteristic $ \neq 2,3$ and $5$. Then we discuss applications to dlt singularities and to Mori fiber spaces of threefolds.

#### 2 Citations

Relative MMP without Q-factoriality.

- Mathematics
- 2020

We consider the minimal model program for varieties that are not Q-factorial. We show that, in many cases, its steps are simpler than expected. In particular, all flips are 1-complemented. The main… Expand

Relative mmp without $ \mathbb{Q} $-factoriality

- Mathematics
- 2021

We consider the minimal model program for varieties that are not \begin{document}$ \mathbb{Q}$\end{document} -factorial. We show that, in many cases, its steps are simpler than expected. The main… Expand

#### References

SHOWING 1-10 OF 31 REFERENCES

A Witt Nadel vanishing theorem for threefolds

- Mathematics
- Compositio Mathematica
- 2020

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, if a projective… Expand

Rational points on log Fano threefolds over a finite field

- Mathematics
- 2015

We prove the $W\mathcal{O}$-rationality of klt threefolds and the rational chain connectedness of klt Fano threefolds over a perfect field of characteristic $p>5$. As a consequence, any klt Fano… Expand

On the Kawamata-Viehweg vanishing for log del Pezzo surfaces in positive characteristic

- Mathematics
- 2020

We prove the Kawamata-Viehweg vanishing theorem on surfaces of del Pezzo type over perfect fields of positive characteristic $p > 5$. As a consequence, we show that klt threefold singularities over a… Expand

Discrepancies of $p$-cyclic quotient varieties

- Mathematics
- 2017

We consider quotient varieties associated to linear representations of the cyclic group of order $p$ in characteristic $p>0$. We give a lower bound of discrepancies of exceptional divisors over these… Expand

Purely Log Terminal Threefolds with Non-Normal Centres in Characteristic Two

- Mathematics
- 2016

abstract:We show that many classical results of the minimal model program do not hold over an algebraically closed field of characteristic two. Indeed, we construct a three dimensional plt pair whose… Expand

ON DEL PEZZO FIBRATIONS IN POSITIVE CHARACTERISTIC

- Mathematics
- 2020

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. Second, we show… Expand

On the rationality of Kawamata log terminal singularities in positive characteristic

- Mathematics
- 2017

We show that there exists a natural number $p_0$ such that any three-dimensional Kawamata log terminal singularity defined over an algebraically closed field of characteristic $p>p_0$ is rational and… Expand

Kawamata-Viehweg vanishing fails for log del Pezzo surfaces in characteristic 3

- Mathematics
- 2017

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 threefold singularity… Expand

Resolution of Singularities of Arithmetical Threefolds II

- Mathematics
- 2014

We prove Grothendieck's Conjecture on Resolution of Singulari-ties for quasi-excellent schemes X of dimension three and of arbitrary characteristic. This applies in particular to X = SpecA, A a… Expand

Small resolutions and non-liftable Calabi-Yau threefolds

- Mathematics
- 2008

We use properties of small resolutions of the ordinary double point in dimension three to construct smooth non-liftable Calabi-Yau threefolds. In particular, we construct a smooth projective… Expand