IJPAM: Volume 57, No. 4 (2009)

FINITELY GENERATED SUBALGEBRAS OF COX RINGS
(CURVES OF HIGHER GENUS AND
EASY ABELIAN SURFACES)

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Let $G \cong \mathbb {Z}^{\oplus s}$, $s \ge 2$, be a free and finitely generated subgroup of $\mbox{Pic}(X)$ with $\dim (\mbox{Pic}(X)) >0$. Here in two cases ($X$ a curve of genus $>0$ and $X$ an Abelian surface with $\mbox{Num}(X) \cong \mathbb {Z}$) we get an exponential measure of non-finitely generation of the commutative ring $\oplus _{L\in G} H^0(X,L)$.

Received: November 11, 2009

AMS Subject Classification: 14H51, 14K99

Key Words and Phrases: Cox ring

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 57
Issue: 4