Tate resolutions for Segre embeddings

Cox, David; Materov, Evgeny

doi:10.2140/ant.2008.2.523

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Tate resolutions for Segre embeddings

David A. Cox and Evgeny Materov

Vol. 2 (2008), No. 5, 523–549

DOI: 10.2140/ant.2008.2.523

Abstract

We give an explicit description of the terms and differentials of the Tate resolution of sheaves arising from Segre embeddings of $ℙ^{a} \times ℙ^{b}$ . We prove that the maps in this Tate resolution are either coming from Sylvester-type maps, or from Bezout-type maps arising from the so-called toric Jacobian.

Keywords

Tate resolution, Segre embedding, toric Jacobian

Mathematical Subject Classification 2000

Primary: 13D02

Secondary: 14M25

Milestones

Received: 14 January 2008

Accepted: 28 May 2008

Published: 4 July 2008

Authors

David A. Cox
Department of Mathematics and Computer Science Amherst College Amherst, MA 01002-5000 United States
http://www.amherst.edu/~dacox
Evgeny Materov
Department of Mathematics and Statistics University of Massachusetts Amherst, MA 01003-9305 United States

Vol. 2, No. 5, 2008