Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-28T16:18:51.203Z Has data issue: false hasContentIssue false
  • English
  • Français

Divisor class groups and graded canonical modules of multisection rings

Published online by Cambridge University Press:  11 January 2016

Kazuhiko Kurano
Kazuhiko Kurano*
Affiliation:
Department of Mathematics, School of Science and Technology, Meiji University, Kawasaki 214-8571, Japan, kurano@isc.meiji.ac.jp
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Keywords

14C2013C20
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 212 , December 2013 , pp. 139 - 157
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2013

References

[1] Bruns, W. and Herzog, J., Cohen–Macaulay Rings, Cambridge Stud. Adv. Math. 39, Cambridge University Press, Cambridge, 1993. MR 1251956.Google Scholar
[2] Elizondo, E. J., Kurano, K., and Watanabe, K.-i., The total coordinate ring of a normal projective variety, J. Algebra 276 (2004), 625–637. MR 2058459. DOI 10.1016/j. jalgebra.2003.07.007.Google Scholar
[3] Goto, S., Nishida, K., and Shimoda, Y., The Gorensteinness of symbolic Rees algebras for space curves, J. Math. Soc. Japan 43 (1991), 465–481. MR 1111598. DOI 10. 2969/jmsj/04330465.CrossRefGoogle Scholar
[4] Hashimoto, M., “Equivariant twisted inverses” in Foundations of Grothendieck Duality for Diagrams of Schemes, Lecture Notes in Math. 1960, Springer, Berlin, 2009, 261–478. MR 2490558. DOI 10.1007/978-3-540-85420-3.Google Scholar
[5] Hashimoto, M. and Kurano, K., The canonical module of a Cox ring, Kyoto J. Math. 51 (2011), 855–874. MR 2854155. DOI 10.1215/21562261-1424884.Google Scholar
[6] Hu, Y. and Keel, S., Mori dream spaces and GIT, Michigan Math. J. 48 (2000), 331–348. MR 1786494. DOI 10.1307/mmj/1030132722.Google Scholar
[7] Matsumura, H., Commutative Ring Theory, Cambridge Stud. Adv. Math. 8, Cambridge University Press, Cambridge, 1986. MR 0879273.Google Scholar
[8] Mori, S., On affine cones associated with polarized varieties, Jpn. J. Math. (N.S.) 1 (1975), 301–309. MR 0439859.Google Scholar
[9] Samuel, P., Lectures on unique factorization domains, Tata Inst. Fund. Res. Stud. Math. 30, Tata Institute of Fundamental Research, Bombay, 1964. MR 0214579.Google Scholar
[10] Shimoda, Y., The class group of the Rees algebras over polynomial rings, Tokyo J. Math. 2 (1979), 129–132. MR 0541902. DOI 10.3836/tjm/1270473564.Google Scholar
[11] Simis, A. and Trung, N. V., The divisor class group of ordinary and symbolic blow-ups, Math. Z. 198 (1988), 479–491. MR 0950579. DOI 10.1007/BF01162869.Google Scholar
[12] Watanabe, K.-i., Some remarks concerning Demazure’s construction of normal graded rings, Nagoya Math. J. 83 (1981), 203–211. MR 0632654.Google Scholar