Frobenius splittings of toric varieties

Abstract

We discuss a characteristic free version of Frobenius splittings for toric varieties and give a polyhedral criterion for a toric variety to be diagonally split. We apply this criterion to show that section rings of nef line bundles on diagonally split toric varieties are normally presented and Koszul, and that Schubert varieties are not diagonally split in general.

11 pages, 2 figures. v3: improved exposition throughout; removed Section 5 due to gap in proof of Theorem 1.5. To appear in Algebra and Number Theory