We study curves on a smooth rational scroll surface S, in particular the multiplicative structure of the Hartshorne–Rao module MC of any curve C ⊂ S. The main result is the construction of the minimal generators of MC . As a consequence, we get that for curves C on a rational normal scroll surface, the Hilbert function of MC determines the module structure. This is a strong form of the converse of the Hartshorne–Schenzel Theorem.
On the structure of the Hartshorne-Rao module of curves on surfaces of minimal degree / DI GENNARO, Roberta. - In: COMMUNICATIONS IN ALGEBRA. - ISSN 0092-7872. - STAMPA. - 33:(2005), pp. 2749-2763.
On the structure of the Hartshorne-Rao module of curves on surfaces of minimal degree
DI GENNARO, ROBERTA
2005
Abstract
We study curves on a smooth rational scroll surface S, in particular the multiplicative structure of the Hartshorne–Rao module MC of any curve C ⊂ S. The main result is the construction of the minimal generators of MC . As a consequence, we get that for curves C on a rational normal scroll surface, the Hilbert function of MC determines the module structure. This is a strong form of the converse of the Hartshorne–Schenzel Theorem.| File | Dimensione | Formato | |
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