![Diameter](https://cmsa.fas.harvard.edu/media/Diameter.jpg)
Over the past few months, CMSA member Valentino Tosatti has authored the following papers. Preprints can be found in ArXiv.
Diameter Bounds for Degenerating Calabi-Yau Metrics
Yang Li and Valentino Tosatti
Abstract. We obtain sharp upper and lower bounds for the diameter of Ricciflat Kähler metrics on polarized Calabi-Yau degeneration families, as conjectured by Kontsevich-Soibelman.
![New Papers by Valentino Tosatti](/media/Diameter-792x1024.png)
Smooth Asymptotics for Collapsing Calabi-Yau Metrics
Hans-Joachin Hein and Valentino Tosatti
Abstract. We prove that Calabi-Yau metrics on compact Calabi-Yau manifolds whose Kähler classes shrink the fibers of a holomorphic fibration have a priori estimates of all orders away from the singular fibers. This follows from a stronger statement which gives an asymptotic expansion of these metrics as the fibers shrink, in terms of explicit functions on the total space and with k-th order remainders that satisfy uniform C k -estimates with respect to a collapsing family of background metrics.
![New Papers by Valentino Tosatti](/media/Smooth-1-792x1024.png)
Canonical Currents and Heights for K3 Surfaces
Simion Filip and Valentino Tosatti
Abstract. We construct canonical positive currents and heights on the boundary of the ample cone of a K3 surface. These are equivariant for the automorphism group and fit together into a continuous family, defined over an enlarged boundary of the ample cone. Along the way, we construct preferred representatives for certain height functions and currents on elliptically fibered surfaces.
![New Papers by Valentino Tosatti](/media/canonical-794x1024.png)