Irish Algebraic Geometry Seminar March 1112, 2011
School of Mathematical
Sciences, University College Cork
This is our second Algebraic
Geometry meeting. The
first was organized by Madeeha Khalid in November 2010. Venue: Western
Gateway Building (a.k.a. IT building, UCC) on Western Road, Cork. Accommodation: Garmish house
on Western Road. Schedule: 
Friday, March 11 

Time 
Speaker

Title

Room

1:00
pm 
Damiano Testa (University
of Oxford) 
Conics
on the Fermat quintic threefold 
WGB
G08 
3:00
pm 
Diane Maclagan (University
of Warwick) 
Tropical
bounds on effective cycles 
WGB
G13 
4:30
pm 
Vijay Singh (University
College Dublin) 
Explicit
HondaTate theorem for supersingular Abelian Varieties 
WGB
G13 
Saturday, March 12 

Time 
Speaker 
Title 
Room

9:00
am 
Madeeha Khalid (St.
Patrick’s College, Drumcondra) 
Azumaya algebras on K3 surfaces 
WGB
106 
Conference
dinner: Friday 6:30pm.
Abstracts:
Damiano
Testa: Conics on the Fermat quintic
threefold
Many
interesting features of algebraic varieties are encoded in the spaces of rational
curves that they contain. For instance,
a smooth cubic surface in complex projective threedimensional space contains
exactly 27 lines; exploiting the configuration of these lines it is possible to
find a (rational) parameterization of the points of the cubic by the points in
the complex projective plane.
After
a general overview, we focus on the Fermat quintic threefold X, namely the
hypersurface in fourdimensional projective space with equation
x^5+y^5+z^5+u^5+v^5=0. The space of
lines on X is wellknown. I will explain
how to use a mix of algebraic geometry, number theory and computerassisted
calculations to study the space of conics on X.
This
talk is based on joint work with R. HeathBrown.
Vijay Singh: Explicit HondaTate theorem for supersingular Abelian Varieties
I
will give the list of characteristic polynomials of supersingular abelian
varieties of dimensions up to 7, and the simple procedure to find them which
can in principle be extended to all dimensions.
Madeeha
Khalid: Azumaya algebras on K3
surfaces
There has been considerable interest in various notions of non commutative geometry in the last decade or so, particularly twisted sheaves on Calabi Yau manifolds, in the context of mathematical physics.
An Azumaya algebra on a variety is essentially a vector bundle of matrices on the variety. It corresponds to a twisted sheaf on the variety and hence is a natural objects to study.
In this talk we will mostly explain a classical example of an Azumaya algebra on a K3 surfaces, and present some of our results about its invariants.
We will conclude with some recent results on moduli spaces of Azumaya algebras on K3 surfaces.