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Transversality theorems in general characteristic and arithmetically Buchsbaum schemes. (English) Zbl 0828.14031
Let \(X\) be a smooth algebraic variety, \(E\) a vector bundle on \(X\) and let \(Y\) be a smooth subvariety of \(X\).
In characteristic 0, if \(V \subset H^0 E\) generates \(E\), then a general member of \(V\) is transversal to \(Y\); this fact is often used to compute the dimension of 0-loci of sections and their singular loci. In characteristic \(p > 0\), transversality may fail. The main result of this paper shows that, on the other hand, if we make the additional hypothesis that \(V\) also generates the sheaf of principal parts of \(E\), then transversality holds in any characteristic. The author uses his result to prove that the classification of arithmetically Buchsbaum curves, found by M. C. Chang, works in positive characteristic, too.
Reviewer: L.Chiantini (Roma)

14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14G15 Finite ground fields in algebraic geometry
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