Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-05-30T05:15:31.980Z Has data issue: false hasContentIssue false
  • English
  • Français

On the structure of generalized Albanese varieties

Published online by Cambridge University Press:  24 October 2008

Hurit nsiper
Hurit nsiper
Affiliation:
Department of Mathematics, Middle East Technical University, Ankara, Turkey
Get access Rights & Permissions [Opens in a new window]

Extract

Given a smooth projective surface X over an algebraically closed field k and a modulus (an effective divisor) m on X, one defines the idle class group Cm(X) of X with modulus m (see 1, chapter III, section 4). The corresponding generalized Albanese variety Gum and the generalized Albanese map um:X|m|Gum have the following universal mapping property (2): if :XG is a rational map into a commutative algebraic group which induces a homomorphism Cm(X)G(k) (1, chapter III, proposition 1), then factors uniquely through um.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 111 , Issue 2 , March 1992 , pp. 267 - 272
Copyright
Copyright © Cambridge Philosophical Society 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1Kato, K. and Saito, S.. Two-dimensional class field theory. In Adv. Stud. Pure Math. no. 2 (1983), pp. 103152.CrossRefGoogle Scholar
2nsipee, H.. On generalized Albanese varieties for surfaces. Math. Proc. Cambridge Philos. Soc. 104 (1988), 16.Google Scholar
3Serre, J. P.. Morphismes Universels el Diffrentiels de Troisime Espce. Sminaire Chevalley, expos no. 11 (1958/1959).Google Scholar