Mld's vs thresholds and flips

关于flip的终止与例外非典范奇点

On termination of flips and exceptionally non-canonical singularities

本文引入并研究了例外非典范（enc）奇点，将flip的终止问题归结为终端flip的终止及enc对mlds的ACC猜想，并在维度3和4中证明了相关结论。

On divisors computing MLD's and LCT's

We show that if a divisor centered over a point on a smooth surface computes a minimal log discrepancy, then the divisor also computes a log canonical threshold. To prove the result, we study the asymptotic log canonical threshold of the graded sequence of ideals associated to a divisor over a variety. We systematically study this invariant and also prove a result describing which divisors compute asymptotic log canonical thresholds.

零附近的 Mld 与 lct

Mld versus lct near zero

研究奇点的最小对数差异与一般超平面截面的对数规范阈值趋近于零的等价性。

曲面上的最优界

Optimal bounds on surfaces

本文证明了曲面的 $\mathbb R$-补阈值、整体对数典范阈值和例外曲面最小 mld 的首个间隙均为 $\frac{1}{13}$，并给出对数曲面最小体积等若干最优界及相关分类结果。

ACC for log canonical thresholds and termination of log flips

We prove that the ascending chain condition (ACC) for log canonical (lc) thresholds in dimension $d$ and Special Termination in dimension $d$ imply the termination of any sequence of log flips starting with a $d$-dimensional lc pair of nonnegative Kodaira dimension. In particular, in characteristic zero, the latter termination in dimension 4 follows from Alexeev-Borisov's conjecture in dimension 3.

Existence of log canonical flips and a special LMMP

Let $(X/Z,B+A)$ be a $\Q$-factorial dlt pair where $B,A\ge 0$ are $\Q$-divisors and $K_X+B+A\sim_\Q 0/Z$. We prove that any LMMP$/Z$ on $K_X+B$ with scaling of an ample$/Z$ divisor terminates with a good log minimal model or a Mori fibre space. We show that a more general statement follows from the ACC for lc thresholds. An immediate corollary of these results is that log flips exist for log canonical pairs.