|Location:||MSRI: Simons Auditorium|
Interplay of real and complex geometry and the Nash conjectures'
Abstract: After recalling the notion of a real variety, both embedded and abstract,
and illustrating it in some elementary case, as the one of complex tori,
we shall point out the importance of real objects for the topological
investigation of complex varieties. The second part will be dedicated to the Nash problem of determining the
topological type of varieties of negative Kodaira dimension.
Starting with Comessatti's theorem on the topology of real rational
surfaces, we shall proceed to sketching Kollar's application of MMP to
this problem, and recent extensions of Comessatti's theorem to 3-folds
obtained in joint work with Frederic Mangolte.