Title: Positivity for higher (co)dimensional numerical cycle classes
Speaker: Mihai Fulger (Princeton University)
Speaker's URL: https://web.math.princeton.edu/~afulger/
Seminar Type: Algebraic Geometry
Abstract: It is classical to study the geometry of a projective variety through positive cones of numerical classes of divisors or curves. The Mori cone in particular plays an important role in the classification of projective algebric varieties. A number of pathological examples have shifted attention from the higher (co)dimensional case. They show that the analogous definitions do not lead to the same positivity properties. To correct the negative outlook, I look at stronger positivity conditions. A sample result is that the pseudoeffective cone of numerical k-dimensional cycle classes is pointed for all k. The proof works in all characteristics, and without restrictions on singularities. This is in joint work with Brian Lehmann.
