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Demazure Construction for Zn-Graded Krull Domains

Yusuke Arai , Ayaka Echizenya , icon-email Kazuhiko Kurano

Abstract

For a Mori dream space X, the Cox ring Cox(X) is a Noetherian Zn-graded normal domain for some n>0. Let C(Cox(X)) be the cone (in Rn) which is spanned by the vectors a∈Zn such that Cox(X)a≠0. Then, C(Cox(X)) is decomposed into a union of chambers. Berchtold and Hausen (Michigan Math. J., 54(3) 483–515: 2006) proved the existence of such decompositions for affine integral domains over an algebraically closed field. We shall give an elementary algebraic proof to this result in the case where the homogeneous component of degree 0 is a field. Using such decompositions, we develop the Demazure construction for Zn-graded Krull domains. That is, under an assumption, we show that a Zn- graded Krull domain is isomorphic to the multi-section ring R(X;D1,…,Dn) for certain normal projective variety X and Q-divisors D1,…,Dn on X.

Viện Toán học, Viện Hàn lâm Khoa học và Công nghệ Việt Nam

Địa chỉ: Số 18 đường Hoàng Quốc Việt, quận Cầu Giấy, Hà Nội

Điện thoại: 024 37563474 - Fax: 024 37564303

Email: vientoan@math.ac.vn

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      • 19. /app/Repositories/Pages/PagesRepository.php:108
      • 20. view::22404baedef17ea59e3ac1e1ef4f69087a37cb5d:31
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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      Metadata
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      Metadata
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      Metadata
      Backtrace
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