Presented By: Student Algebraic Geometry Seminar - Department of Mathematics
Student Algebraic Geometry: Anti-Canonical Divisors on Frobenius Split Varieties
Barry Henaku
For our settling, let X be a normal variety over a field of characteristic p. It can be shown that every \mathcal{O}_{X}-linear map \phi:F_{*}^{e}\mathcal{O}_{X}\to\mathcal{O}_{X} corresponds to an effective divisor D_{\phi}\in |(1-p^{e})K_{X}| and hence to an effective anti-canonical Q-divisor. For this talk, we plan on using this correspondence to study test ideals for pairs and compatibly split subschemes.