124 citations · 2k across the 80 of their papers we have counts for
6 papers · 1 filter
Regularity of the volume function
Junyu Cao, Valentino Tosatti
We prove the optimal regularity of the volume function on the big cone of a projective manifold, and investigate its regularity when restricted to segments moving in ampl…
The volume of a divisor and cusp excursions of geodesics in hyperbolic manifolds
Simion Filip, John Lesieutre, Valentino Tosatti
We give a complete description of the behavior of the volume function at the boundary of the pseudoeffective cone of certain Calabi-Yau complete intersections known as Wehler N-fol…
Special Kähler geometry and holomorphic Lagrangian fibrations
Yang Li, Valentino Tosatti
Given a holomorphic Lagrangian fibration of a compact hyperkahler manifold, we use the differential geometry of the special Kahler metric that exists on the base away from the disc…
Nakamaye's theorem on complex manifolds
Valentino Tosatti
We discuss Nakamaye's Theorem and its recent extension to compact complex manifolds, together with some applications.
Families of Calabi-Yau manifolds and canonical singularities
Valentino Tosatti
Given a polarized family of varieties over the unit disc, smooth except over the origin and with smooth fibers Calabi-Yau, we show that the origin lies at finite Weil-Petersson dis…
Triviality of fibered Calabi-Yau manifolds without singular fibers
Valentino Tosatti, Yuguang Zhang
In this note we show that if a compact Kahler manifold with trivial canonical bundle is the total space of a holomorphic fibration without singular fibers, then the fibration is a…