Higher dimensional slope inequalities
Friday, 7.5.21, 10:30-11:30, virtueller Raum 404
onsider a family of varieties f: X-> T, where T is a curve. We prove several inequalities about the slope of f, which are generalisations of Xiao and Cornalba-Harris inequalities in the case where X is a surface. We then apply our results to the KSB moduli space of stable varieties to study the ample cone of such spaces.\nThe talk is based on a joint work with Giulio Codogni and Filippo Viviani.
Highly connected 7-manifolds and non-negative sectional curvature
Friday, 14.5.21, 10:30-11:30, virtueller Raum Lasker
A six-parameter family of highly connected 7-manifolds which admit an SO(3)-invariant metric of non-negative sectional curvature is constructed and the Eells-Kuiper invariant of each is computed. In particular, it follows that all exotic spheres in dimension 7 admit an SO(3)-invariant metric of non-negative curvature.
Valuation rings in the context of Algebraic Geometry
Thursday, 20.5.21, 11:15-12:15, online: kasparov
Cox rings of algebraic stacks
Friday, 21.5.21, 10:30-11:30, virtueller Raum Lasker
In this talk, I will discuss the construction of Cox rings on algebraic\nstacks. Recall that the Cox ring consists of all global sections of\ndivisors on a given space. Here the definition of the multiplicative\nstructure is a bit subtle. But it turns out that such a structure\nalways exists, and moreover, its (non-)uniqueness can be measured by an\nExt-group. This talk is based on a joint work with Elena Martinengo and\nFabio Tonini.