Codimension one foliations with numerically trivial canonical class on singular spaces

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 result of Loray, Pereira and Touzet to this context

On Fano varieties whose effective divisors are numerically eventually free

In this paper we classify mildly singular Fano varieties with maximal Picard number whose effective divisors are numerically eventually free.Comment: A few typos and an issue in Lemma 4.6 are fixe

The Zariski-Lipman conjecture for log canonical spaces

In this paper we prove the Zariski-Lipman conjecture for log canonical spaces.Comment: 8 page

Some remarks on regular foliations with numerically trivial canonical class

In this article, we first describe codimension two regular foliations with numerically trivial canonical class on complex projective manifolds whose canonical class is not numerically effective. Building on a recent algebraicity criterion for leaves of algebraic foliations, we then address regular foliations of small rank with numerically trivial canonical class on complex projective manifolds whose canonical class is pseudo-effective. Finally, we confirm the generalized Bondal conjecture formulated by Beauville in some special cases.Comment: 20 page