An optimal boundedness on weak $\bQ$-Fano threefolds

Jungkai Alfred Chen; Meng Chen

arxiv: 0712.4356 · v2 · submitted 2007-12-28 · 🧮 math.AG

An optimal boundedness on weak bQ-Fano threefolds

Jungkai Alfred Chen , Meng Chen This is my paper

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keywords boundfanoloweroptimalproveweakanti-canonicalboundedness

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Let $X$ be a terminal weak $\bQ$-Fano threefold. We prove that $P_{-6}(X)>0$ and $P_{-8}(X)>1$. We also prove that the anti-canonical volume has a universal lower bound $-K_X^3 \geq 1/330$. This lower bound is optimal.

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An optimal boundedness on weak bQ-Fano threefolds

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