COW seminar
The COW
Algebraic Geometry seminar meets at a convenient place: usually Cambridge,
Oxford, Warwick, Bath or London.
The main organiser is Gregory Sankaran at Bath.
Next meeting
London, Thursday 15th June 2017
2:00 Timothy Logvinenko (Cardiff): Pfunctors 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.
Social programme
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.
>
Abstracts

Logvinenko
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 nonsplit Pfunctor. This is a joint work with Rina Anno (Kansas).

Sierra
In the ongoing programme to classify noncommutative projective
surfaces (connected graded noetherian domains of GelfandKirillov
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 P^{2}) is minimal, and that this has strong
ringtheoretic implications: surprisingly, a Sklyanin algebra has no
birational connected graded noetherian overrings.
This is joint work with Dan Rogalski and Toby Stafford.
gks@maths.bath.ac.uk
Artwork by Sketch the Cow
(sketch@cow.net)