Abstract
The Monoid M(X) of homology classes of effective cycles of codimension 1 on an n-dimensional complex torus X is characterized in terms of 2n × 2n integer matrices. Examples of tori X are constructed for which M(X) is finitely generated, as well as examples for which finite generation fails. In particular, it is shown that for "general" products X of elliptic curves, M(X) is finitely generated, while for Abelian varieties of the singular type, finite generation of the monoid fails.
Partially supported by Illinois State University re-assigned research time.
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© 1981 Springer-Verlag
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Rosoff, J.A. (1981). The monoid of effective divisor classes on a complex torus. In: Libgober, A., Wagreich, P. (eds) Algebraic Geometry. Lecture Notes in Mathematics, vol 862. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090893
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DOI: https://doi.org/10.1007/BFb0090893
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