Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON A COMPUTATION OF PLURIGENUS OF A CANONICAL THREEFOLD

  • Received : 2015.03.05
  • Published : 2016.01.31
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Abstract

For a canonical threefold X, it is known that $p_n$ does not vanish for a sufficiently large n, where $p_n=h^0(X,\mathcal{O}_X(nK_X))$. We have shown that $p_n$ does not vanish for at least one n in {6, 8, 10}. Assuming an additional condition $p_2{\geq}1$ or $p_3{\geq}1$, we have shown that $p_{12}{\geq}2$ and $p_n{\geq}2$ for $n{\geq}14$ with one possible exceptional case. We have also found some inequalities between ${\chi}(\mathcal{O}_X)$ and $K^3_X$.

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References

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