• Corpus ID: 240354646

Positivity of the Moduli Part

  title={Positivity of the Moduli Part},
  author={Florin Ambro and Paolo Cascini and Vyacheslav Vladimirovich Shokurov and Calum Spicer},
We prove the Cone Theorem for algebraically integrable foliations. As a consequence, we show that termination of flips implies the b-nefness of the moduli part of a log canonical pair with respect to a contraction, generalising the case of lc trivial fibrations. 

On semi-ampleness of the moduli part

. We discuss a conjecture of Shokurov on the semi-amplenes of the moduli part of a general fibration.

MMP for algebraically integrable foliations

We show that termination of flips for $\mathbb Q$-factorial klt pairs in dimension $r$ implies existence of minimal models for algebraically integrable foliations of rank $r$ with log canonical

Log adjunction: moduli part

    V. Shokurov
    Известия Российской академии наук. Серия математическая
  • 2023
Upper moduli part of adjunction is introduced and its basic property are discussed. The moduli part is b-Cartier in the case of rational multiplicities and is b-nef in the maximal case. Bibliography:

Uniform rational polytopes of foliated threefolds and the global ACC

In this paper, we show the existence of uniform rational lc polytopes for foliations with functional boundaries in dimension $\leq 3$. As an application, we prove the global ACC for foliated

On the canonical bundle formula in positive characteristic

Let $f: X \rightarrow Z$ be a fibration from a normal projective variety $X$ of dimension $n$ onto a normal curve $Z$ over a perfect field of characteristic $p>2$. Let $(X, B)$ be a log canonical

The locus of log canonical singularities

The LCS locus is an essential ingredient in the proof of fundamental results of Log Minimal Model Program, such as nonvanishing and base point freeness theorems. We prove in this paper that the LCS

Codimension 1 foliations with numerically trivial canonical class on singular spaces

    S. Druel
    Duke Mathematical Journal
  • 2021
In this article, we describe the structure of codimension one foliations with canonical singularities and numerically trivial canonical class on varieties with terminal singularities, extending a

Log adjunction: moduli part

Upper moduli part of adjunction is introduced and its basic property are discussed. The moduli part is b-Cartier in the case of rational multiplicities and is b-nef in the maximal case. Bibliography:

Towards the second main theorem on complements

We prove the boundedness of complements modulo two conjectures: Borisov–Alexeev conjecture and effective adjunction for fibre spaces. We discuss the last conjecture and prove it in two particular

On foliations with nef anti-canonical bundle

In this paper we prove that the anti-canonical bundle of a holomorphic foliation $\mathcal{F}$ on a complex projective manifold cannot be nef and big if either $\mathcal{F}$ is regular, or

Log Adjunction: effectiveness and positivity

This is a first instalment of much larger work about relations between birational geometry and moduli of triples. The extraction of work is mainly related to Theorem 6. It is a weak version of

Characterization of generic projective space bundles and algebraicity of foliations

In this paper we consider various notions of positivity for distributions on complex projective manifolds. We start by analyzing distributions having big slope with respect to curve classes,

Higher-dimensional foliated Mori theory

We develop some foundational results in a higher-dimensional foliated Mori theory, and show how these results can be used to prove a structure theorem for the Kleiman–Mori cone of curves in terms of

Singularities of the minimal model program

Preface Introduction 1. Preliminaries 2. Canonical and log canonical singularities 3. Examples 4. Adjunction and residues 5. Semi-log-canonical pairs 6. Du Bois property 7. Log centers and depth 8.

Varieties fibered by good minimal models

Let f : X → Y be an algebraic fiber space such that the general fiber has a good minimal model. We show that if f is the Iitaka fibration or if f is the Albanese map with relative dimension no more