Next Meeting

University of Kent - Thursday 14th June

There will be a meeting of the COW at the University of Kent, in Canterbury, on Thursday 14th June. All talks will be held in room SR3 of the Sibson building; a map may be found here. The schedule will be as follows.

Schedule

Time Speaker Title
1:30pm Fedor Bogomolov Torsion Points of Elliptic Curves and Applications to Geometry of Arithmetic Curves
3:00pm Sara Filippini Orbital Degeneracy Loci and Applications
4:30pm Miles Reid The Tate-Oort Group and Godeaux Surfaces in Mixed Characteristic

Abstracts

Fedor Bogomolov (Courant Institute, New York and Higher School of Economics, Moscow) - Torsion Points of Elliptic Curves and Applications to Geometry of Arithmetic Curves

Let E be an elliptic curve over the complex numbers having a standard degree 2 projection E -> P1 to the projective line, with ramification the 2-torsion points of E. I consider the subset P(E) in P1 given as the projection of all the torsion points of E. For two different curves, P(E) and P(E') intersect in a finite set, in many cases in just 1 point.

In the most interesting case when E is defined over a subfield of Qbar, I use an iterative process based on P(E) to construct a nontrivial infinite algebraic extension of the field Q(j(E)), where j(E) is the j-invariant of E, which depends on Q(j(E)) and is strictly smaller than Qbar.

I consider some applications of results on the properties of the P(E) and their subsets to construction of unramified correspondences between curves of higher genus defined over arithmetic and finite fields. Compare arXiv:1706.01586.

Sara Filippini (Imperial) - Orbital Degeneracy Loci and Applications
We consider a generalization of degeneracy loci of morphisms between vector bundles based on orbit closures of algebraic groups in their linear representations. Using a certain crepancy condition on the orbit closure we gain some control over the canonical sheaf in a preferred class of examples. This is notably the case for Richardson nilpotent orbits and partially decomposable skew-symmetric three-forms in six variables. We show how these techniques can be applied to construct Calabi-Yau manifolds and Fano varieties of dimension three and four. This is joint work with Vladimiro Benedetti, Laurent Manivel and Fabio Tanturri.
Miles Reid (Warwick) - The Tate-Oort Group and Godeaux Surfaces in Mixed Characteristic
Abstract forthcoming.

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