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Some observations on subschemes of codimension 1 of a projective variety. (Italian) Zbl 0613.14009

Let X be a projective variety, Y a Weil divisor on X. When is Y a hypersurface section? In case X is a plane curve of degree \(d\) B. Segre proved the answer to be positive if the degree of Y is convenient \((=fd)\) and Y does not impose independent conditions on curves of degree \(d+f-3.\)
A cohomological proof of this result allows to extend the result to the case where X is arithmetically Cohen-Macaulay and subcanonical \((\omega_ X\cong {\mathcal O}_ X(a))\), and indeed to more general situations.
Reviewer: F.Catanese

MSC:

14C20 Divisors, linear systems, invertible sheaves
14M07 Low codimension problems in algebraic geometry
14M10 Complete intersections
14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
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