Algebra Seminar

Let C be a (usually singular) curve in the projective plane. For over a century it has been known explicitly how to embed the nonsingular model of C in some other projective space. This is the method of adjoint curves. It also makes explicit many other calculations on curves. I will show how it works, and how to interpret it in a way suited to calculations already present in the magma computer algebra system. This approach also allows one to make a proof of the main results about adjoint curves in the style of modern birational geometry, that is, using linear systems and vanishing theorems.

(Note that Gavin Brown is an algebraic geometer and not the Vice-Chancellor.))