Cheltsov Ivan
1School of Mathematics, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD UK.
Laboratory of Algebraic Geometry, GU-HSE, 6 Usacheva street, Moscow, Russia 119048.
J Geom Anal. 2017;27(3):2302-2338. doi: 10.1007/s12220-017-9762-y. Epub 2017 Feb 7.
We prove that and are the smallest log canonical thresholds of reduced plane curves of degree , and we describe reduced plane curves of degree whose log canonical thresholds are these numbers. As an application, we prove that and are the smallest values of the -invariant of Tian of smooth surfaces in of degree . We also prove that every reduced plane curve of degree whose log canonical threshold is smaller than is GIT-unstable for the action of the group , and we describe GIT-semistable reduced plane curves with log canonical thresholds .
我们证明了 和 是次数为 的约化平面曲线的最小对数典范阈值，并且我们描述了次数为 且对数典范阈值为这些数的约化平面曲线。作为一个应用，我们证明了 和 是次数为 的 中光滑曲面的田 - 不变量的最小值。我们还证明了每个次数为 且对数典范阈值小于 的约化平面曲线对于群 的作用是 GIT - 不稳定的，并且我们描述了对数典范阈值为 的 GIT - 半稳定约化平面曲线。
