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The ring of global sections of multiples of a line bundle on a toric variety
Author(s):
E.
Javier
Elizondo
Journal:
Proc. Amer. Math. Soc.
125
(1997),
2527-2529.
MSC (1991):
Primary 14C20, 14M25
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Abstract:
In this article we prove that for any complete toric variety, and for any Cartier divisor, the ring of global sections of multiples of the line bundle associated to the divisor is finitely generated.
References:
- [Bat93]
- Victor V. Batyrev. Variations of the mixed hodge structure of affine hypersurfaces in algebraic tori. Duke Math. J., 69(2):349-409, Feb 1993. MR 94m:14067
- [Cox95]
- David A. Cox. The homogeneous coordinate ring of a toric variety. J. Algebraic Geom., 4(3):17-50, 1995. MR 95i:14046
- [CS93]
- S. D. Cutkosky and V. Srinivas. On a problem of Zariski on dimensions of linerar systems. Ann. of Math., 137:531-559, 1993. MR 94g:14001
- [Dan78]
- V. I. Danilov. The geometry of toric varieties. Russian Math. Surveys, 33(2):97-154, 1978. MR 80g:14001
- [Zar62]
- O. Zariski. The theorem of Riemann-Roch for high multiples of an effective divisor on an algebraic surface. Ann. of Math., 76:560-616, 1962. MR 25:5065
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Additional Information:
E.
Javier
Elizondo
Affiliation:
Instituto de Matemáticas, UNAM, Ciudad Universitaria, México D.F. 04510
Email:
javier@math.unam.mx
DOI:
10.1090/S0002-9939-97-03918-X
PII:
S 0002-9939(97)03918-X
Received by editor(s):
March 14, 1996
Additional Notes:
Supported in part by grant CONACYT 3936-E, and DGAPA IN101296
Communicated by:
Ron Donagi
Copyright of article:
Copyright
1997,
American Mathematical Society
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