Nagoya Mathematical Journal

Divisor class groups and graded canonical modules of multisection rings

Kazuhiko Kurano

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Abstract

We describe the divisor class group and the graded canonical module of the multisection ring T(X;D1,,Ds) for a normal projective variety X and Weil divisors D1,,Ds on X under a mild condition. In the proof, we use the theory of Krull domain and the equivariant twisted inverse functor.

Article information

Source
Nagoya Math. J., Volume 212 (2013), 139-157.

Dates
First available in Project Euclid: 5 September 2013

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1378386543

Digital Object Identifier
doi:10.1215/00277630-2366323

Mathematical Reviews number (MathSciNet)
MR3290682

Zentralblatt MATH identifier
1298.14011

Subjects
Primary: 14C20: Divisors, linear systems, invertible sheaves
Secondary: 13C20: Class groups [See also 11R29]

Citation

Kurano, Kazuhiko. Divisor class groups and graded canonical modules of multisection rings. Nagoya Math. J. 212 (2013), 139--157. doi:10.1215/00277630-2366323. https://projecteuclid.org/euclid.nmj/1378386543


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References

  • [1] W. Bruns and J. Herzog, Cohen–Macaulay Rings, Cambridge Stud. Adv. Math. 39, Cambridge University Press, Cambridge, 1993.
  • [2] E. J. Elizondo, K. Kurano, and K.-i. Watanabe, The total coordinate ring of a normal projective variety, J. Algebra 276 (2004), 625–637.
  • [3] S. Goto, K. Nishida, and Y. Shimoda, The Gorensteinness of symbolic Rees algebras for space curves, J. Math. Soc. Japan 43 (1991), 465–481.
  • [4] M. Hashimoto, “Equivariant twisted inverses” in Foundations of Grothendieck Duality for Diagrams of Schemes, Lecture Notes in Math. 1960, Springer, Berlin, 2009, 261–478.
  • [5] M. Hashimoto and K. Kurano, The canonical module of a Cox ring, Kyoto J. Math. 51 (2011), 855–874.
  • [6] Y. Hu and S. Keel, Mori dream spaces and GIT, Michigan Math. J. 48 (2000), 331–348.
  • [7] H. Matsumura, Commutative Ring Theory, Cambridge Stud. Adv. Math. 8, Cambridge University Press, Cambridge, 1986.
  • [8] S. Mori, On affine cones associated with polarized varieties, Jpn. J. Math. (N.S.) 1 (1975), 301–309.
  • [9] P. Samuel, Lectures on unique factorization domains, Tata Inst. Fund. Res. Stud. Math. 30, Tata Institute of Fundamental Research, Bombay, 1964.
  • [10] Y. Shimoda, The class group of the Rees algebras over polynomial rings, Tokyo J. Math. 2 (1979), 129–132.
  • [11] A. Simis and N. V. Trung, The divisor class group of ordinary and symbolic blow-ups, Math. Z. 198 (1988), 479–491.
  • [12] K.-i. Watanabe, Some remarks concerning Demazure’s construction of normal graded rings, Nagoya Math. J. 83 (1981), 203–211.