On the spectrum of certain subschemes of \(\mathbb{P}^N\)
In projective geometry usually one considers graded algebras generated by elements of degree 1. Here the author considers a natural case in which more general objects occur (e.g. \(\bigoplus_{n\geq 0}H^0(C, {\mathcal O}_C(1))\) with \(C\) a locally Cohen-Macaulay even unreduced curve or, more generally, a quasi \(ACM\) subscheme \(\mathbb{P}^N)\) and studies subschemes of \(\mathbb{P}^N\) (in arbitrary characteristic) whwhich correspond to equi-dimensional Cohen-Macaulay algebras, \(A\), such that \(A\) modulo the subalgebra generated by the elements of degree 1 has finite length. The author studies the spectrum of these algebras following the theory of the spectrum for torsion free sheaves of \(\mathbb{P}^N\) previously introduced by himself. The results concern the \(h\)-vector of the algebra \(A\) in terms of the index of speciality and the number of generators in each degree of the Rao module of \(C\).
scientific article; zbMATH DE number 1308322