On the structure of the Hartshorne – Rao module of curves on surfaces of minimal degree. (English) Zbl 1079.14041
Let \(S \subset \mathbb{P}^n\) be a rational ruled surface and \(C \subset S\) an integral curve. Here the author studies the Hartshorne-Rao module \(M_C\) of \(C\). She constructs the minimal generators of \(M_C\). In particular she computes the index of regularity of \(C\). When \(S\) is a rational normal scroll she obtains a strong form of the converse of a theorem of Hartshorne and Schenzel [cf.
P. Schenzel, in: Commutative algebra, singularities and computer algebra. Proc. NATO adv. res. workshop, Sinaia, 2002 (Dordrecht: Kluwer Academic Publishers), NATO Sci. Ser. II, Math. Phys. Chem. 115, 225–239 (2003; Zbl 1056.14055)].
Reviewer: Edoardo Ballico (Povo)
MSC:
| 14H50 | Plane and space curves |
| 14J26 | Rational and ruled surfaces |
| 14C20 | Divisors, linear systems, invertible sheaves |
| 14M06 | Linkage |
Citations:
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