On a computation of plurigenus of a canonical threefold
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For a canonical threefold $X$, it is known that $p_n$ does not vanish for a sufficiently large $n$, where $p_n=h^0(X,\cx(nK_X))$. 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 $\ex$ and $\kx$.
Abstract
For a canonical threefold $X$, it is known that $p_n$ does not vanish for a sufficiently large $n$, where $p_n=h^0(X,\cx(nK_X))$. 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 $\ex$ and $\kx$.
참고문헌 (6)
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