Computational Algebra Seminar: Brown -- The Picard group of del Pezzo surfaces

We have computed with divisors on curves for a decade.                          
Analogous calculations are possible using curves on surfaces                    
(rather than points on curves) with many new phenomena.                         
Del Pezzo surfaces are the 2-dimensional analogues                              
of conic curves. Their divisor class groups are lattices                        
Z^d, where the bilinear form comes from the intersection                        
of curves on a surface. The basic geometrical theory is                         
available in magma, and I want to explain that and then                         
show how it relates to some arithmetic properties of surfaces.                  
This has plenty of relations to what Martin and Steve have                      
been doing recently, to Mike's sheaf code and to John Cremona's                 
code for conic curves over a function field; for comparison later,              
Andrew is working on similar theory but with an added                           
finite group action.