论文标题
KLT的猜想最小的体积
Klt varieties of conjecturally minimal volume
论文作者
论文摘要
我们构建具有丰富规范类别和最小卷的KLT投影品种。我们还发现具有最小已知的抗态量的非凡klt Fano品种。我们猜想我们的示例在每个维度上的体积最小，我们为此提供了低维的证据。为了改善较早的示例，我们被迫考虑不是准平滑的加权性超曲面。我们证明，通过计算其全球日志规范阈值（或$α$ - invariant），我们的Fano品种是出色的；它非常大，大约$ 2^{2^n} $ in Dimension $ n $。这些示例在Birkar定理中提供了有关Fano品种补充的界限。
We construct klt projective varieties with ample canonical class and the smallest known volume. We also find exceptional klt Fano varieties with the smallest known anticanonical volume. We conjecture that our examples have the smallest volume in every dimension, and we give low-dimensional evidence for that. In order to improve on earlier examples, we are forced to consider weighted hypersurfaces that are not quasi-smooth. We show that our Fano varieties are exceptional by computing their global log canonical threshold (or $α$-invariant) exactly; it is extremely large, roughly $2^{2^n}$ in dimension $n$. These examples give improved lower bounds in Birkar's theorem on boundedness of complements for Fano varieties.
