Back to Algebraic Geometry Seminar: Spring 2013
Algebraic Geometry Seminar
Date: Wednesday, Apr 10, 2013
Time: 3:30PM - 4:30PM
Location: LCB 215
(Wednesday) Time/Location: 2pm - 3pm JTB 320
Mark De Cataldo
SUNY, Stony Brook
Title |
The projectors of the decomposition theorem are absolute Hodge |
Abstract |
I report on joint work with Luca Migliorini at Bologna. If you have a map of complex projective manifolds, then the rational cohomology of the domain splits into a direct sum of pieces in a way dictated by the singularities of the map. By Poincare’ duality, the corresponding projections can be viewed as cohomology classes (projectors) on the self-product of the domain. These projectors are Hodge classes, i.e. rational and of type (p,p) for the Hodge decomposition. Take the same situation after application of an automorphism of the ground field of complex numbers. The new projectors are of course Hodge classes. On the other hand, you can also transplant, using the field automorphism, the old projectors into the new situation and it is not clear that the new projectors and the transplants of the old projectors coincide. We prove they do, thus proving that the projectors are absolute Hodge classes, i.e. their being of Hodge type survives the totally discontinuous process of a field automorphism. We also prove that these projectors are motivated in the sense of Andre. |
Algebraic Geometry