Greco, Silvio Some observations on subschemes of codimension 1 of a projective variety. (Italian) Zbl 0613.14009 Semin. Geom., Univ. Studi Bologna 1985, 89-100 (1986). 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 Cited in 1 Review 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) Keywords:Weil divisor; hypersurface section; arithmetically Cohen-Macaulay PDFBibTeX XMLCite \textit{S. Greco}, Semin. Geom., Univ. Studi Bologna 1985, 89--100 (1986; Zbl 0613.14009)