Functional Analysis and Its Applications

, Volume 47, Issue 3, pp 210–226 | Cite as

Syzygy algebras for Segre embeddings



We describe the syzygy spaces for the Segre embedding ℙ(U) × ℙ(V) ⊂ ℙ(UV) in terms of representations of GL(U) × GL(V) and construct the minimal resolutions of the sheaves
(a, b) in D(ℙ(UV)) for a ⩽ −dim(U) and b ⩽ −dim(V). We also prove a property of multiplication in syzygy spaces of the Segre embedding.

Key words

syzygy algebra Koszul cohomology representations of GL Segre embedding derived category of coherent sheaves 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Mathematical Department of Higher School of EconomicsMoscow Independent University of MoscowMoscowRussia

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