Non-archimedean links of singularities
Friday, 8.1.16, 10:15-11:15, Raum 404, Eckerstr. 1
I will introduce a non-archimedean version of the link of a singularity. This object will be a space of valuations, a close relative of non-archimedean analytic spaces (in the sense of Berkovich) over trivially valued fields. \nAfter describing the structure of these links, I will deduce information about the resolutions of surface singularities. \nIf times allows, I will then characterize those normal surface singularities whose link satisfies a self-similarity property. The last part is a current work in progress with Charles Favre and Matteo Ruggiero.
Classifying line bundles over rigid analytic varieties
Friday, 15.1.16, 10:15-11:15, Raum 404, Eckerstr. 1
Degenerations of polarized Calabi-Yau manifolds
Friday, 22.1.16, 10:00-11:00, Raum 404, Eckerstr. 1
I will present a joint work with Mattias Jonsson in which we rely on non-Archimedean geometry to study the limit behavior of the volume forms of Ricci-flat Kähler metrics in a degenerating family.
Frobenius splittings in birational geometry
Friday, 29.1.16, 10:15-11:15, Raum 404, Eckerstr. 1
Frobenius splittings in birational geometry
Friday, 29.1.16, 10:15-11:15, Raum 404, Eckerstr. 1
Due to the absence of the Kawamata-Viehweg vanishing theorem, the classification of algebraic varieties in positive characteristic, as of very recently, has been seen as an insurmountable task. Recent progress in the field has been inspired by the discovery of Frobenius-split varieties. In my talk, I will discuss connections between the geometry of projective varieties and properties of the Frobenius action, focusing particularly on surfaces.