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Syzygy algebras for Segre embeddings

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Abstract

We describe the syzygy spaces for the Segre embedding ℙ(U) × ℙ(V) ⊂ ℙ(U ⊗ V) in terms of representations of GL(U) × GL(V) and construct the minimal resolutions of the sheaves

(a, b) in D(ℙ(U ⊗ V)) for a ⩽ −dim(U) and b ⩽ −dim(V). We also prove a property of multiplication in syzygy spaces of the Segre embedding.

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Authors and Affiliations

  1. Mathematical Department of Higher School of Economics, Moscow Independent University of Moscow, Moscow, Russia

    I. V. Netay

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  1. I. V. Netay
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Correspondence to I. V. Netay.

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__________

Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 47, No. 3, pp. 54–74, 2013

Original Russian Text Copyright © by I. V. Netay

This work was partially supported by AG Laboratory HSE, RF government grant no. 11.G34.31.0023, RFBR grants nos. 10-01-00836 and 12-01-31012, RF government grants nos. MK-3312.2012.1 and MK-6612.2012.1, and the Simons Foundation.

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Netay, I.V. Syzygy algebras for Segre embeddings. Funct Anal Its Appl 47, 210–226 (2013). https://doi.org/10.1007/s10688-013-0027-7

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  • DOI: https://doi.org/10.1007/s10688-013-0027-7

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