대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제25권2호
  • /
  • Pages.161-165
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  • 2010
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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ON A NONVANISHING OF PLURIGENUS OF A THREEFOLD OF GENERAL TYPE

  • 발행 : 2010.04.30
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초록

Even though there is a formula for $h^0$(X, $\cal{O}_X(nK_X)$) for a canonical threefold X, it is not easy to compute $h^0$(X, $\cal{O}_X(nK_X)$) because the formula has a term due to singularities. In this paper, we find a way to control the term due to singularities. We show nonvanishing of plurigenus for the case when the index r in the singularity type $\frac{1}{r}$(1, -1, b) is sufficiently large.

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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. 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.
  3. D.-K. Shin, On a computation of plurigenera of a canonical threefold, J. Algebra 309 (2007), no. 2, 559-568. https://doi.org/10.1016/j.jalgebra.2006.03.034