10 papers
Foliated Minimal Models and Flops
Paolo Cascini, Roktim Mascharak, Calum Spicer
We study minimal models and flops for foliations. We show that if is a rank one foliation with canonical singularities on a normal projective -factorial var…
Relative semi-ampleness in positive characteristic
Paolo Cascini, Hiromu Tanaka
Given an invertible sheaf on a fibre space between projective varieties of positive characteristic, we show that fibrewise semi-ampleness implies relative semi-ampleness. The same…
Birational boundedness of stable families
Paolo Cascini, Jihao Liu, Calum Spicer +1
We prove that normal projective stable families of maximal variation, of fixed dimension, and with bounded adjoint volume are birationally bounded. This is a consequence of a subst…
A Matsushima theorem for K-polystable polarised smooth Fano threefolds
Hamid Abban, Paolo Cascini, Ivan Cheltsov
We prove that if is a smooth Fano threefold and is an ample -divisor such that is K-polystable, then the automorphism group is r…
Recent progress on the Minimal Model Program for foliations
Paolo Cascini, Calum Spicer
We survey recent progress on the birational geometry of foliations on complex varieties. We focus on the MMP viewpoint: singularities, adjunction and applications to the MMP for fo…
On base point freeness for rank one foliations
Paolo Cascini, Calum Spicer
We prove the base point free theorem for log canonical foliated pairs of rank one on a Q-factorial projective klt threefold. Moreover, we show abundance in the case of numerically…