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arXiv 2004.022802020-04-09math.AGmath.AC

Biliaison of sheaves

Mengyuan Zhang

备注：: 21 pages, added a reference by Burragina that treats a special case of our theory

英文摘要：

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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