Algebraic Geometry seminar meets at a convenient place: usually Cambridge,
Oxford, Warwick, Bath or London.
The main organiser is Gregory Sankaran at Bath.
London, Thursday 15th June 2017
2:00 Timothy Logvinenko (Cardiff): P-functors and cyclic covers
3:30 Susan Sierra (Edinburgh): The birational geometry of noncommutative projective surfaces
The talks will be in Room 340 of the Huxley Building, Imperial College.
The preferred pub in
London is the Queen's Arms,
across the road in Queen's Gate Mews,
but a decision about where to go
will be made on the day by those present.
I will begin by reviewing the geometry of a cyclic cover branched in a
divisor. I will then explain how it gives us the first ever example of
a non-split P-functor. This is a joint work with Rina Anno (Kansas).
In the ongoing programme to classify noncommutative projective
surfaces (connected graded noetherian domains of Gelfand-Kirillov
dimension three) a natural first step is to try to understand birational
transformations. One then asks: is there a noncommutative analogue of
contracting a (-1)-curve? What are the minimal models within
a birational class? It is not even clear a priori what the
correct definition is of a minimal model in this context.
Beginning with an elliptic algebra (roughly, a noncommutative
analogue of a Fano surface), we describe how to blow up a point and
how to contract a (-1)-curve. We use this technology to show that a
generic Sklyanin algebra (a noncommutative version
of P2) is minimal, and that this has strong
ring-theoretic implications: surprisingly, a Sklyanin algebra has no
birational connected graded noetherian overrings.
This is joint work with Dan Rogalski and Toby Stafford.
Artwork by Sketch the Cow