Let k be an algebraically closed field and let C be a nonhyperelliptic smooth projective curve of genus g defined over k. Since the canonical model of C is arithmetically Gorenstein, Macaulay’s theory of inverse systems allows us to associate to C a cubic form f in the divided power k-algebra Rg−3 in g − 2 variables. The apolarity ap(C) of C is the minimal number t of linear form in Rg−3 needed to write f as the sum of their divided power cubes. It is easy to see that ap(C) is at least g − 2 and P. De Poi and F. Zucconi classified curves with ap(C) = g −2 when k is the complex number field. In this paper, we give a complete, characteristic free, classification of curves C with apolarity g −1 (and g −2).
Canonical curves with low apolarity / Ballico, Edoardo; G., Casnati; R., Notari. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 332:1(2011), pp. 229-243.
Titolo: | Canonical curves with low apolarity |
Autori: | Ballico, Edoardo; G., Casnati; R., Notari |
Autori Unitn: | |
Titolo del periodico: | JOURNAL OF ALGEBRA |
Anno di pubblicazione: | 2011 |
Numero e parte del fascicolo: | 1 |
Codice identificativo Scopus: | 2-s2.0-79952188214 |
Codice identificativo ISI: | WOS:000288353300012 |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jalgebra.2010.12.030 |
Handle: | http://hdl.handle.net/11572/86323 |
Citazione: | Canonical curves with low apolarity / Ballico, Edoardo; G., Casnati; R., Notari. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 332:1(2011), pp. 229-243. |
Appare nelle tipologie: | 03.1 Articolo su rivista (Journal article) |
File in questo prodotto:
File | Descrizione | Tipologia | Licenza | |
---|---|---|---|---|
YJABR13251.pdf | Versione editoriale (Publisher’s layout) | Tutti i diritti riservati (All rights reserved) | Administrator |