Vol. 3, No. 1, 2009

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Frobenius splittings of toric varieties

Sam Payne

Vol. 3 (2009), No. 1, 107–119

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.

Frobenius splitting, toric variety, diagonal splitting, Koszul
Mathematical Subject Classification 2000
Primary: 14M25
Secondary: 13A35, 14M15, 16S37
Received: 8 May 2008
Revised: 15 October 2008
Accepted: 22 November 2008
Published: 1 February 2009
Sam Payne
Department of Mathematics
Building 380, Sloan Hall
Stanford University
Stanford, CA 94305
United States