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Vanishing of sections of vector bundles on 0-dimensional schemes. (English) Zbl 1013.14006
Given a vector bundle \(F\) (spanned by global sections) on an integral projective variety \(X\), the author considers a 0-dimensional subscheme \(Z\) of \(X\) formed by a union of general fat points and studies the rank of the restriction map \(r_{F,Z}:H^0(X,F)\to H^0(Z,F|Z)\), namely the surjectivity and injectivity of the map. The considerations are presented on examples, and the existence of rank \(2\) reflexive sheaves on \(\mathbb{P}^3\) satisfying special conditions is proved.
MSC:
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
14F17 Vanishing theorems in algebraic geometry
14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
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