The ring of global sections of multiples of a line bundle on a toric variety
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- by E. Javier Elizondo
- Proc. Amer. Math. Soc. 125 (1997), 2527-2529
- DOI: https://doi.org/10.1090/S0002-9939-97-03918-X
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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
- Victor V. Batyrev, Variations of the mixed Hodge structure of affine hypersurfaces in algebraic tori, Duke Math. J. 69 (1993), no. 2, 349–409. MR 1203231, DOI 10.1215/S0012-7094-93-06917-7
- David A. Cox, The homogeneous coordinate ring of a toric variety, J. Algebraic Geom. 4 (1995), no. 1, 17–50. MR 1299003
- S. D. Cutkosky and V. Srinivas, On a problem of Zariski on dimensions of linear systems, Ann. of Math. (2) 137 (1993), no. 3, 531–559. MR 1217347, DOI 10.2307/2946531
- V. I. Danilov, The geometry of toric varieties, Uspekhi Mat. Nauk 33 (1978), no. 2(200), 85–134, 247 (Russian). MR 495499
- Oscar Zariski, The theorem of Riemann-Roch for high multiples of an effective divisor on an algebraic surface, Ann. of Math. (2) 76 (1962), 560–615. MR 141668, DOI 10.2307/1970376
Bibliographic Information
- E. Javier Elizondo
- Affiliation: Instituto de Matemáticas, UNAM, Ciudad Universitaria, México D.F. 04510
- Email: javier@math.unam.mx
- 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 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 2527-2529
- MSC (1991): Primary 14C20, 14M25
- DOI: https://doi.org/10.1090/S0002-9939-97-03918-X
- MathSciNet review: 1401739