Deutsch
 
Hilfe Datenschutzhinweis Impressum
  DetailsucheBrowse

Datensatz

DATENSATZ AKTIONENEXPORT
  Cycle relations on Jacobian varieties. With an appendix by Don Zagier.

van der Geer, G., & Kouvidakis, A. (2007). Cycle relations on Jacobian varieties. With an appendix by Don Zagier. Compositio Mathematica, 143(4), 900-908.

Item is

Basisdaten

einblenden: ausblenden:
Genre: Zeitschriftenartikel

Externe Referenzen

einblenden:

Urheber

einblenden:
ausblenden:
 Urheber:
van der Geer, Gerard1, Autor           
Kouvidakis, Alexis2, Autor
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              
2Max Planck Society, ou_persistent13              

Inhalt

einblenden:
ausblenden:
Schlagwörter: -
 Zusammenfassung: Let X be an abelian variety over an algebraically closed field. \it A. Beauville showed [Math. Ann. 273, 647--651 (1986; Zbl 0566.14003)] that the Chow ring \textCH\Bbb Q(X) of X with rational coefficients has a double grading \textCH\Bbb Q(X)=\bigoplus \textCH^i(j)(X), where \textCH^i(j)(X)=x\in \textCH^i(X);k^*(x)= k^2i-jx for any k\in \bbfZ. Furthermore the quotient A(X) modulo algebraic equivalence inherits the double grading: A(X)=\bigoplus A^i(j)(X). Accordingly, when X is the Jacobian variety of a curve C of genus g, the class [C]\in A^g-1(X) of the image of the Abel-Jacobi mapping is decomposed as [C]=\sum^g-1j=0C(j) with C(j)\in A(j)^g-1(X). \par \it E. Colombo and \it B. van Geemen [Compos. Math. 88, No. 3, 333--353 (1993; Zbl 0802.14002)], proved that for a d-gonal curve the components C(j) vanish for j≥ d-1. Moreover, \it F. Herbaut [Compos. Math. 143, No. 4, 883--899 (2007; Zbl 1187.14006)] extended this and found cycle relations for curves having a g^rd. The main result of this paper gives simpler relations than Herbaut's and shows that \suma1+⋅s+ ar=N(a1+1)!\dots(ar+1)! C(a1)*⋅s*C(ar)=0 for N≥ d-2r+1, where ``*" denotes the Pontryagin product. In an appendix by Zagier, their relations are shown to be equivalent.

Details

einblenden:
ausblenden:
Sprache(n):
 Datum: 2007
 Publikationsstatus: Erschienen
 Seiten: -
 Ort, Verlag, Ausgabe: -
 Inhaltsverzeichnis: -
 Art der Begutachtung: -
 Identifikatoren: eDoc: 744870
Anderer: 111
 Art des Abschluß: -

Veranstaltung

einblenden:

Entscheidung

einblenden:

Projektinformation

einblenden:

Quelle 1

einblenden:
ausblenden:
Titel: Compositio Mathematica
Genre der Quelle: Zeitschrift
 Urheber:
Affiliations:
Ort, Verlag, Ausgabe: London Mathematical Society, London; Cambridge University Press, Cambridge
Seiten: - Band / Heft: 143 (4) Artikelnummer: - Start- / Endseite: 900 - 908 Identifikator: ISSN: 0010-437X