Frobenius splittings of toric varieties

Payne, Sam

doi:10.2140/ant.2009.3.107

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Frobenius splittings of toric varieties

Sam Payne

Vol. 3 (2009), No. 1, 107–119

DOI: 10.2140/ant.2009.3.107

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.

Keywords

Frobenius splitting, toric variety, diagonal splitting, Koszul

Mathematical Subject Classification 2000

Primary: 14M25

Secondary: 13A35, 14M15, 16S37

Milestones

Received: 8 May 2008

Revised: 15 October 2008

Accepted: 22 November 2008

Published: 1 February 2009

Authors

Sam Payne
Department of Mathematics Building 380, Sloan Hall Stanford University Stanford, CA 94305 United States

Vol. 3, No. 1, 2009