On the defining equations of subvarieties in \(\mathbb P^n\). (English) Zbl 0601.14041
The author gives an upper bound for the degrees of the generators of an homogeneous ideal defining a (generically reduced) subscheme \(X\subset {\mathbb{P}}^n\), by using an invariant which depends on the length of the cohomology \(H^i({\mathbb{P}}^n,{\mathcal J}_X(n))\), \(n>-\dim X\), where \({\mathcal J}_X\) is the ideal sheaf of \(X\) in \({\mathbb{P}}^n\).
Reviewer: M. Herrmann (Köln)
MSC:
14M10 | Complete intersections |
14A05 | Relevant commutative algebra |
14C99 | Cycles and subschemes |
14M05 | Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) |