Special Colloquium
Mihnea Popa
University of Chicago
Vanishing theorems and Fourier-Mukai functors
Abstract: Vanishing theorems are one of the essential tools of modern
algebraic geometry, and have particularly important applications in higher
dimensional geometry. Under strong positivity assumptions, there are
well-known "standard" vanishing theorems, like those of Kodaira and
Kawamata-Viehweg. They have very useful partial analogues, called Generic
Vanishing Theorems - first discovered by Green and Lazarsfeld - when the
positivity hypotheses on line bundles are weakened. I will describe all of
the above and their importance, and then explain that abstract
Fourier-Mukai functors and homological algebra can be used to relate
generic vanishing theorems to standard vanishing theorems, and in
particular generalize the results of Green-Lazarsfeld to a version of
Kodaira vanishing under weak positivity hypotheses.
Thursday December 7, 2006 at 3:30 PM in SEO 636