Compactifying moduli of line bundles on curves
Joseph Harris (Harvard University)
MSRI: Simons Auditorium
The problem discussed in this talk is to compactify the moduli space of pairs (C,L) with C a smooth projective curve of genus g and L a line bundle of degree d on C. Such a compactification was first found by Caporaso a quarter century ago, but there is an obstruction to the existence of a universal family over it. We'll describe this obstruction, and attempts by Ran and Mainò to deal with it.