28 citations · 202 across the 25 of their papers we have counts for
25 papers
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…
Deformations of fibered Calabi--Yau varieties
Benjamin Bakker, Kristin DeVleming, Stefano Filipazzi +5
Kollár showed that small deformations of elliptically fibered smooth -torsion varieties with remain elliptically fibered. We extend this result to any f…
Characterization of products of projective spaces via nef complexity
Joshua Enwright, Stefano Filipazzi, Yoshinori Gongyo +4
We define the nef complexity of a projective variety . This invariant compares with the sum of the coefficients of nef partitions of . We prove that the nef…
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…
Variation of algebraically integrable adjoint foliated structures
Paolo Cascini, Jihao Liu, Fanjun Meng +2
Given a canonical algebraically integrable foliation on a klt projective variety, we study the variation of the ample models of the associated adjoint foliated structures with resp…
Moduli of surfaces fibered in log Calabi-Yau pairs
Giovanni Inchiostro, Roberto Svaldi, Junyan Zhao
We study the moduli spaces of surface pairs admitting a log Calabi--Yau fibration . We develop a series of results on stable reduction and apply them to give a…
Boundedness of some fibered K-trivial varieties
Philip Engel, Stefano Filipazzi, François Greer +2
We prove that irreducible Calabi-Yau varieties of a fixed dimension, admitting a fibration by abelian varieties or primitive symplectic varieties of a fixed analytic deformation cl…
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…
Boundedness of elliptic Calabi-Yau threefolds
Stefano Filipazzi, Christopher D. Hacon, Roberto Svaldi
We show that elliptic Calabi--Yau threefolds form a bounded family. We also show that the same result holds for minimal terminal threefolds of Kodaira dimension 2, upon fixing the…
A geometric characterization of toric singularities
Joaquín Moraga, Roberto Svaldi
Given a projective contraction and a log canonical pair such that is nef over a neighborhood of a closed point , one can define…
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…
Rational curves and strictly nef divisors on Calabi--Yau threefolds
Haidong Liu, Roberto Svaldi
We give a criterion for a nef divisor to be semiample on a Calabi--Yau threefold when and . As a direct consequence, we show that on suc…
Boundedness of elliptic Calabi-Yau varieties with a rational section
Caucher Birkar, Gabriele Di Cerbo, Roberto Svaldi
We show that for each fixed dimension , the set of -dimensional klt elliptic varieties with numerically trivial canonical bundle is bounded up to isomorphism in codimen…
On the connectedness principle and dual complexes for generalized pairs
Stefano Filipazzi, Roberto Svaldi
Let be a pair, and let be a contraction with nef over . A conjecture, known as the Shokurov-Kollár connectedness principle, predi…
The Jordan property for local fundamental groups
Lukas Braun, Stefano Filipazzi, Joaquín Moraga +1
We show the Jordan property for regional fundamental groups of klt singularities of fixed dimension. Furthermore, we prove the existence of effective simultaneous index one covers…
Invariance of Plurigenera and boundedness for Generalized Pairs
Stefano Filipazzi, Roberto Svaldi
In this note, we survey some recent developments in birational geometry concerning the boundedness of algebraic varieties. We delineate a strategy to extend some of these results t…
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…
Birational boundedness of rationally connected Calabi-Yau 3-folds
Weichung Chen, Gabriele Di Cerbo, Jingjun Han +2
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…
A note on the fibres of Mori fibre spaces
Giulio Codogni, Andrea Fanelli, Roberto Svaldi +1
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…
Effective algebraic integration in bounded genus
Jorge Vitorio Pereira, Roberto Svaldi
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.…
Birational boundedness of low dimensional elliptic Calabi-Yau varieties with a section
Gabriele Di Cerbo, Roberto Svaldi
We prove that there are finitely many families, up to isomorphism in codimension one, of elliptic Calabi-Yau manifolds with a rational section, provided that $\dim…
A geometric characterisation of toric varieties
Morgan Brown, James McKernan, Roberto Svaldi +1
We prove a conjecture of Shokurov which characterises toric varieties using log pairs.
Hyperbolicity for log canonical pairs and the cone theorem
Roberto Svaldi
Given a log canonical pair , we show that is nef assuming there is no non-constant map from the affine line with values in the open strata of the stratification ind…