Arithmetic Study Group: Resolution of singularities
4 November 2010 16:15 in CM219
Resolution of singularities is a topic in Algebraic Geometry that has classical appeal and is also a current area of research. In 1964 Heisuke Hironaka proved that all varieties over a field of characteristic zero can be resolved, and went on to receive the Fields medal for this work. We will look at the basic techniques of resolution, and use them to outline proofs of resolution for curves and surfaces which demonstrate the basic idea behind Hironaka's proof. We will also give an overview of current progress in extending the proof to positive characteristic.