Algebraic Geometry Seminar

How much of the geometry of a positive characteristic variety is encoded in its Frobenius? I’ll give exact answers to this vague question in the toric case. For this, I’ll introduce a Frobenius-theoretic cone sitting inside the pseudo-effective cone whose interaction with the other nef/ample/big cones determines the type of extremal contractions a variety can undergo. This leads to a geometric characterization of when the kernel of the Frobenius trace is; respectively, big, ample, and nef. This talk is based on my joint work with Emre Özavci (EPFL), arXiv:2506.02994.