# On the numerical dimension of pseudo-effective divisors in positive characteristic

Tuesday, November 6, 2012 -

4:30pm to 6:00pm

Suppose that X is a smooth algebraic variety over an algebraically closed field and that D is a pseudo effective R-divisor on X. In characteristic zero, by utilizing vanishing theorems, Nakayama proved that if D is not numerically equivalent to the negative part of its Zariski decomposition, then D is pseudo-effective. We prove the same result in characteristic p > 0 using the Frobenius morphism as a replacement for vanishing theorems. This is joint work with Paolo Cascini, Christopher Hacon and Mircea Mustata.

Speaker:

Karl Schwede

Penn State University

Event Location:

Fine Hall 322