On codimension 1 del Pezzo foliations on varieties with mild singularities

Abstract

In this paper we extend to the singular setting the theory of Fano foliations developed in our previous paper. A Q-Fano foliation on a complex projective variety X is a foliation F whose anti-canonical class is an ample Q-Cartier divisor. In the spirit of Kobayashi-Ochiai Theorem, we prove that under some conditions the index i of a Q-Fano foliation is bounded by the rank r of F, and classify the cases in which i=r. Next we consider Q-Fano foliations F for which i=r-1. These are called del Pezzo foliations. We classify codimension 1 del Pezzo foliations on mildly singular varieties.

20 pages, to appear in Mathematische Annalen

References in corpus (3)

• Differential Forms on Log Canonical Spaces
• Cohomological characterizations of projective spaces and hyperquadrics
• On Fano foliations 2

Cited by in corpus (3)

• Singular rationally connected surfaces with non-zero pluri-forms
• Del Pezzo foliations with log canonical singularities
• Singular rationally connected threefolds with non-zero pluri-forms