Regular del Pezzo surfaces with irregularity

Tuesday, February 5, 2013 -
4:30pm to 6:00pm
Over perfect fields, the geometry of regular del Pezzo surfaces has been classified, but over imperfect fields, the problem remains largely open.  We construct the first examples of regular del Pezzo surfaces X that have positive irregularity h^1(X, O_X ) > 0.  Our construction is by quotienting a regular, quasi-linear surface (i.e. a regular variety that is geometrically a non-reduced first-order neighborhood of a plane) by explicit rank 1 foliations. We also find a restriction on the integer pairs that are possible as the anti-canonical degree and irregularity of such surfaces.
Zachary Maddock
Columbia University
Event Location: 
Fine Hall 322