Daily Archives: February 18, 2009

Direct Image Sheaves Under Proper Maps

Today we continue our review/introduction of background material en route to stating and proving the Riemann Roch theorem. This theorem involves the relationship between proper maps and sheaves on the domain and target, so we need to understand how they … Continue reading

Posted in AG From the Beginning, Algebraic Geometry, Cohomology | 7 Comments

Deligne and Mumford on the Moduli of Curves

Today I’m going to talk a bit about an important paper from 1969.  This one.  It’s a bit hard to read at some points, but it was revolutionary.  In it, Pierre Deligne and David Mumford prove that the moduli space … Continue reading

Posted in Algebraic Geometry, Big Theorems, Curves, Deformation Theory | 3 Comments