대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제27권1호
  • /
  • Pages.37-46
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  • 2012
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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ON THE PLURIGENUS OF A CANONICAL THREEFOLD

  • 투고 : 2010.09.09
  • 발행 : 2012.01.31
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초록

It is well known that plurigenus does not vanish for a sufficiently large multiple on a canonical threefold over $\mathbb{C}$. There is Reid Fletcher formula for plurigenus. But, unlike in the case of surface of general type, it is not easy to compute plurigenus. In this paper, we in-duce a different version of Reid-Fletcher formula and show that the constant term in the induced formula has periodic properties. Using these properties we have an application to nonvanishing of plurigenus.

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참고문헌

  1. A. R. Fletcher, Contributions to Riemann-Roch on projective 3-folds with only canonical singularities and applications, Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), 221-231, Proc. Sympos. Pure Math., 46, Part 1, Amer. Math. Soc., Providence, RI, 1987.
  2. M. Hanamura, Stability of the pluricanonical maps of threefolds, Algebraic geometry, Sendai, 1985, 185-205, Adv. Stud. Pure Math., 10, North-Holland, Amsterdam, 1987.
  3. Y. Kawamata, On the plurigenera of minimal algebraic 3-folds with $K\:{\equiv}\:0$, Math. Ann. 275 (1986), no. 4, 539-546. https://doi.org/10.1007/BF01459135
  4. Y. Miyaoka, The Chern classes and Kodaira dimension of a minimal variety, Algebraic geometry, Sendai, 1985, 449-476, Adv. Stud. Pure Math., 10, North-Holland, Amsterdam, 1987.
  5. M. Namba, Geometry of Projective Algebraic Curves, Monographs and Textbooks in Pure and Applied Mathematics, 88. Marcel Dekker, Inc., New York, 1984.
  6. M. Reid, Young person's guide to canonical singularities, Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), 345-414, Proc. Sympos. Pure Math., 46, Part 1, Amer. Math. Soc., Providence, RI, 1987.
  7. D.-K. Shin, On a computation of plurigenera of a caninical threefold, J. Algebra. 309 (2007), no. 2, 559-568. https://doi.org/10.1016/j.jalgebra.2006.03.034