42 citations · 81 across the 20 of their papers we have counts for
19 papers · 1 filter
MMP for smooth co-rank one foliations
Paolo Cascini, Calum Spicer
We prove the existence of minimal models for smooth co-rank one foliations of general type.
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…
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…
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…
Rank one foliations on toroidal varieties
Calum Spicer, Luca Tasin
Consider a log canonical pair such that there is a Cartier divisor for which is locally free and globally generated. Let $\mathcal…
On moduli of foliated surfaces
Calum Spicer, Roberto Svaldi, Sebastian Velazquez
The birational geometry of foliations exhibits phenomena that are fundamentally different than the case of varieties and that complicate the construction of a satisfactory moduli t…
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…
On finite generation and boundedness of adjoint foliated structures
Paolo Cascini, Jingjun Han, Jihao Liu +4
We prove the existence of good minimal models for any klt algebraically integrable adjoint foliated structure of general type, and that Fano algebraically integrable adjoint foliat…
Minimal model program for algebraically integrable adjoint foliated structures
Paolo Cascini, Jingjun Han, Jihao Liu +4
For -factorial klt algebraically integrable adjoint foliated structures, we prove the cone theorem, the contraction theorem, and the existence of flips. Therefore, we de…
Foliation adjunction
Paolo Cascini, Calum Spicer
We present an adjunction formula for foliations on varieties and we consider applications of the adjunction formula to the cone theorem for rank one foliations and the study of fol…
MMP for algebraically integrable foliations
Paolo Cascini, Calum Spicer
We show that termination of flips for -factorial klt pairs in dimension implies existence of minimal models for algebraically integrable foliations of rank with…
On semi-ampleness of the moduli part
Stefano Filipazzi, Calum Spicer
We discuss a conjecture of Shokurov on the semi-ampleness of the moduli part of a general fibration.
Positivity of the Moduli Part
Florin Ambro, Paolo Cascini, Vyacheslav Shokurov +1
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 p…
Effective generation for foliated surfaces: results and applications
Calum Spicer, Roberto Svaldi
We explore the birational structure and invariants of a foliated surface in terms of the adjoint divisor , . We then establish a b…
On the MMP for rank one foliations on threefolds
Paolo Cascini, Calum Spicer
We prove existence of flips for log canonical foliated pairs of rank one on a Q-factorial projective klt threefold. This, in particular, provides a proof of the existence of a mini…
Local and global applications of the Minimal Model Program for co-rank one foliations on threefolds
Calum Spicer, Roberto Svaldi
We provide several applications of the minimal model program to the local and global study of co-rank one foliations on threefolds. Locally, we prove a singular variant of Malgrang…
MMP for co-rank one foliations on threefolds
Paolo Cascini, Calum Spicer
We prove existence of flips, special termination, the base point free theorem and, in the case of log general type, the existence of minimal models for F-dlt foliated pairs of co-r…
Hypersurfaces quasi-invariant by codimension one foliations
Jorge Vitorio Pereira, Calum Spicer
We present a variant of the classical Darboux-Jouanolou Theorem. Our main result provides a characterization of foliations which are pull-backs of foliations on surfaces by rationa…
Higher dimensional foliated Mori theory
Calum Spicer
We develop some basic 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…