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Roberto Svaldi

Publications and source records attributed to Roberto Svaldi.

25 records · Page 2Linked to original sources
arXiv2021

Local and global applications of the Minimal Model Program for co-rank one foliations on threefolds

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 Malgrange's theorem, a classification of terminal foliation singularities and the existence of separatrices for log canonical singularities. Globally, we prove termination of flips, a connectedness theorem on lc centres, a non-vanshing theorem and some hyperbolicity properties of foliations.

math.AG↗
arXiv2020

Birational boundedness of rationally connected Calabi-Yau 3-folds

We prove that rationally connected Calabi--Yau 3-folds with kawamata log terminal (klt) singularities form a birationally bounded family, or more generally, rationally connected $3$-folds of $ε$-CY type form a birationally bounded family for $ε>0$. Moreover, we show that the set of $ε$-lc log Calabi--Yau pairs $(X, B)$ with coefficients of $B$ bounded away from zero is log bounded modulo flops. As a consequence, we deduce that rationally connected klt Calabi--Yau $3$-folds with mld bounded away from $1$ are bounded modulo flops.

math.AG↗
arXiv2020

Rational curves and strictly nef divisors on Calabi--Yau threefolds

We give a criterion for a nef divisor $D$ to be semiample on a Calabi--Yau threefold $X$ when $D^3=0=c_2(X)\cdot D$ and $c_3(X)\neq 0$. As a direct consequence, we show that on such a variety $X$, if $D$ is strictly nef and $ν(D)\neq 1$, then $D$ is ample; we also show that if there exists a nef non-ample divisor $D$ with $D\not\equiv 0$, then $X$ contains a rational curve when its topological Euler characteristic is not $0$.

math.AG↗
arXiv2019

Effective algebraic integration in bounded genus

We introduce and study birational invariants for foliations on projective surfaces built from the adjoint linear series of positive powers of the canonical bundle of the foliation. We apply the results in order to investigate the effective algebraic integration of foliations on the projective plane. In particular, we describe the Zariski closure of the set of foliations on the projective plane of degree d admitting rational first integrals with fibers having geometric genus bounded by g.

math.AG↗
arXiv2018

A note on the fibres of Mori fibre spaces

In this note we consider the problem of determining which Fano manifolds can be realised as fibres of a Mori fibre space. In particular, we study the case of toric varieties, Fano manifolds with high index and some Fano manifolds with high Picard rank.

math.AG↗
arXiv2015

Fano varieties in Mori fibre spaces

We show that being a general fibre of a Mori fibre space is a rather restrictive condition for a Fano variety. More specifically, we obtain two criteria (one sufficient and one necessary) for a Q-factorial Fano variety with terminal singularities to be realised as a fibre of a Mori fibre space, which turn into a characterisation in the rigid case. We apply our criteria to figure out this property up to dimension three and on rational homogeneous spaces. The smooth toric case is studied and an interesting connection with K-semistability is also investigated.

math.AG↗