On the structure of local cohomology modules for monomial curves in
| Autor: | F. Curtis, L. T. Hoa, M. Fiorentini, H. Bresinsky |
|---|---|
| Rok vydání: | 1994 |
| Předmět: |
Sheaf cohomology
Discrete mathematics Pure mathematics Monomial 010308 nuclear & particles physics General Mathematics Group cohomology 010102 general mathematics Local cohomology 01 natural sciences Cup product 0103 physical sciences ComputingMethodologies_DOCUMENTANDTEXTPROCESSING De Rham cohomology Equivariant cohomology 0101 mathematics GeneralLiterature_REFERENCE(e.g. dictionaries encyclopedias glossaries) Čech cohomology Mathematics |
| Zdroj: | Nagoya Mathematical Journal. 136:81-114 |
| ISSN: | 2152-6842 0027-7630 |
| Popis: | Our setting for this paper is projective 3-spaceover an algebraically closed fieldK. By a curveC⊂is meant a 1-dimensional, equidimensional projective algebraic set, which is locally Cohen-Macaulay. Letbe the Hartshorne-Rao module of finite length (cf. [R]). HereZis the set of integers andℐcthe ideal sheaf ofC. In [GMV] it is shown that, whereis the homogeneous ideal ofC,is the first local cohomology module of theR-moduleMwith respect to. Thus there exists a smallest nonnegative integerk∊Nsuch that, (see also the discussion on the 1-st local cohomology module in [GW]). Also in [GMV] it is shown thatk= 0 if and only ifCis arithmetically Cohen-Macaulay andCis arithmetically Buchsbaum if and only ifk≤ 1. We therefore have the following natural definition. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|