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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 $\kx$.
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참고문헌 (6)
참고문헌 신청
J. A. Chen / 2010 / Explicit birational geometry of threefolds of general type, I / Ann. Sci. ´Ec. Norm. Sup´er 43(3):365~394
J. A. Chen / 2010 / Explicit birational geometry of 3-folds of general type, II / J. Differential Geom 86(2):237~271
A. R. Fletcher / 1987 / Contributions to Riemann-Roch on Projective 3-folds with Only Canon-ical Singularities and Applications, In Algebraic geometry / Proc. Sympos. Pure Math.
J. Kollar / 1986 / Higher direct images of dualizing sheaves I / Ann. of Math 123(1):11~42
M. Reid / 1987 / Young Person’s guide to canonical singularities, In Algebraic geometry / Proc. Sympos. Pure Math. 46:345~414
J. A. Chen / 2010 / Explicit birational geometry of 3-folds of general type, II / J. Differential Geom 86(2):237~271
A. R. Fletcher / 1987 / Contributions to Riemann-Roch on Projective 3-folds with Only Canon-ical Singularities and Applications, In Algebraic geometry / Proc. Sympos. Pure Math.
J. Kollar / 1986 / Higher direct images of dualizing sheaves I / Ann. of Math 123(1):11~42
M. Reid / 1987 / Young Person’s guide to canonical singularities, In Algebraic geometry / Proc. Sympos. Pure Math. 46:345~414
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