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

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

2007-12-28

arxiv.org/abs/0712.4356v2

Advances in Mathematics 219 (2008), 2086-2104

Mathematics

Algebraic Geometry

Scientific paper

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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