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Biliaison of sheaves

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Abstract

We define an equivalence relation among coherent sheaves on a projective variety called biliaison. We prove the existence of sheaves that are minimal in a biliaison class in a suitable sense, and show that all sheaves in the same class can be obtained from a minimal one using certain deformations and other basic moves. Our results generalize the main theorems of liaison theory of subvarieties to sheaves, and provide a framework to study sheaves and subvarieties simultaneously.

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  1. Department of Mathematics, University of California, Berkeley, CA, 94720, USA

    Mengyuan Zhang

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  1. Mengyuan Zhang
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Zhang, M. Biliaison of sheaves. Math. Z. 298, 861–881 (2021). https://doi.org/10.1007/s00209-020-02648-9

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  • DOI: https://doi.org/10.1007/s00209-020-02648-9

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