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Details van artikel 7 van 21 gevonden artikelen
| Titel: |
Compressed gorenstein modules: artin modules of type one having extremal Hilbert functions |
| Auteur: |
Miri, Abderrahim |
| Verschenen in: |
Communications in algebra |
| Paginering: | Jaargang 21 (1993) nr. 8 pagina's 2837-2857 |
| Jaar: |
1993 |
| Inhoud: |
It was known that the various higher partial derivatives of a set of c general enough polynomials [image omitted] of specified degrees are as independent as possible. We generalize this result to a set of c general enough elements of the direct sum Ps. The power series ring [image omitted] acts as partial differential operators on Ps; the Matlis duality relates A-submodules [image omitted] of Ps and quotients M¯ of As. The degrees of [image omitted] determine the socle type of M¯ . A quotient M¯ of As is termed compressed if it has maximal length given {r,s, socle type of M¯}. A compressed module M¯ is the Matlis dual to a set of elements [image omitted] of specified degrees in Ps, whose partial derivatives of all orders are as independent as possible. We term a quotient M¯ of As Gorenstein of socle type tj if its Matlis dual is generated by a single polynomial b of degree j we use the Matlis duality to construct and describe the varietiesG(j) and Z(j) parametrizing the compressed graded and nongradedGorenstein Artin modules M¯ of socle type tj, that are quotientsof M = As. We determine the Hilbert series of such modules andshow that they are termwise extremal among the Hilbert series ofquotients of M having the same socle type. We also determine thedimensions of G(j) and Z(j)i and we show that they are locallyaffine spaces. We apply the dimension result to show, when r = 3 and s = 2,that there is a length-S26 type-one (Gorenstein) quotient M¯ of A⊕A having no deformation to [image omitted] . Thus, M¯ is not smoothable.This complements the result of H. Kleppe that when r = 3 and s = 1, Gorenstein Artin algebra quotients of A are smoothable. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 7 van 21 gevonden artikelen
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