Related papers: On Fano foliations 2
In this paper we address Fano foliations on complex projective varieties. These are foliations whose anti-canonical class is ample. We focus our attention on a special class of Fano foliations, namely del Pezzo foliations on complex…
In this paper, we classify del Pezzo foliations on projective manifolds of rank at least 3 and with log canonical singularities in the sense of McQuillan.
In this paper we study the geometry of mildly singular Fano varieties on which there is an effective prime divisor of Picard number one. Afterwards, we address the case of toric varieties. Finally, we treat the lifting of extremal…
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 this paper we investigate codimension one Fano distributions on Fano manifolds with Picard number one. We classify Fano distributions of maximal index on complete intersections in weighted projective spaces, Fano contact manifolds,…
We study Fano threefolds with Picard number one equipped with a holomorphic section in $\Omega_V^1(1)$.
Let X be a complex Fano manifold of arbitrary dimension, and D a prime divisor in X. We consider the image H of N_1(D) in N_1(X) under the natural push-forward of 1-cycles. We show that the codimension c of H in N_1(X) is at most 8.…
We classify all 1-nodal degenerations of smooth Fano threefolds with Picard number 1 (both nonfactorial and factorial) and describe their geometry. In particular, we describe a relation between such degenerations and smooth Fano threefolds…
We classify the irreducible components of the space of foliations on Fano 3-folds with rank one Picard group. As a corollary we obtain a classification of holomorphic Poisson structures on the same class of 3-folds.
We classify smooth Fano manifolds X with the Picard number $\rho_X \geq 3$ such that there exists an extremal ray which has a birational contraction that maps a divisor to a point.
We give some bounds on the anticanonical degrees of Fano varieties with Picard number 1 and mild singularities, extending results of Koll\'ar et al. from the early 90's and improving them even in the smooth case. The proof is based on a…
We study sextic del Pezzo surface fibrations via root stacks.
In this paper we prove that a regular foliation on a complex weak Fano manifold is algebraically integrable.
This paper describes the structure of singular codimension one foliations with numerically trivial canonical bundle on projective manifolds.
We classify mildly singular Fano varieties $X$ such that $\mathrm{Nef}(X)=\mathrm{Psef}(X)$ and that the Picard number of $X$ is equal to the dimension of $X$ minus $1$.
In this paper we classify mildly singular Fano varieties with maximal Picard number whose effective divisors are numerically eventually free.
We study codimension one holomorphic foliations on complex projective spaces and compact manifolds under the assumption that the foliation has a projective transverse structure in the complement of some invariant codimension one analytic…
We study the Picard variety of the Fano surface of nodal and mildly cuspidal cubic threefolds in arbitrary characteristic by relating divisors on the Fano surface to divisors on the symmetric product of a curve of genus 4.
We study the syzygetic structure of projections of del Pezzo surfaces in order to construct singular Calabi-Yau threefolds. By smoothing those threefolds, we obtain new examples of Calabi-Yau threefolds with Picard group of rank 1. We also…
We study singular del Pezzo surfaces that are quasi-smooth and well-formed weighted hypersurfaces. We give an algorithm how to classify all of them.