Related papers: Minimal log discrepancies on a fixed threefold
We completely prove the ACC for minimal log discrepancies on smooth threefolds. It implies on smooth threefolds the ACC for a-lc thresholds, the uniform m-adic semi-continuity of minimal log discrepancies and the boundedness of the log…
On smooth threefolds, the ACC for minimal log discrepancies is equivalent to the boundedness of the log discrepancy of some divisor which computes the minimal log discrepancy. We reduce it to the case when the boundary is the product of a…
We prove that the ACC conjecture for minimal log discrepancies holds for threefolds in $[1-\delta,+\infty)$, where $\delta>0$ only depends on the coefficient set. We also study Reid's general elephant for pairs, and show Shokurov's…
We generalize the rationality theorem of the accumulation points of log canonical thresholds which was proved by Hacon, M\textsuperscript{c}Kernan, and Xu. Further, we apply the rationality to the ACC problem on the minimal log…
The second largest accumulation point of the set of minimal log discrepancies of threefolds is $\frac{5}{6}$. In particular, the minimal log discrepancies of $\frac{5}{6}$-lc threefolds satisfy the ACC.
We prove the ideal-adic semi-continuity of minimal log discrepancies on surfaces.
In this paper, we show that Shokurov's conjectures on the ACC for $a$-lc thresholds and the ACC for minimal log discrepancies are equivalent in the interval $[0,1)$. That is, the conjecture on ACC for $a$-lc thresholds holds for every…
We prove the ACC conjecture for local volumes. Moreover, when the local volume is bounded away from zero, we prove Shokurov's ACC conjecture for minimal log discrepancies.
For a fixed pair and fixed exponents, we prove the discreteness of log discrepancies over all log canonical triples formed by attaching a product of ideals with given exponents.
We show the existence of prime divisors computing minimal log discrepancies in positive characteristic except for a special case. Moreover we prove the lower semicontinuity of minimal log discrepancies for smooth varieties in positive…
We show that log canonical thresholds satisfy the ACC
We survey the known and expected properties of the minimal log discrepancy, the local invariant of a log variety.
We discuss the ACC conjecture and the LSC conjecture for minimal log discrepancies of generalized pairs. We prove that some known results on these two conjectures for usual pairs are still valid for generalized pairs. We also discuss the…
We give an upper bound for the minimal discrepancies of hypersurface singularities. As an application, we show that Shokurov's conjecture is true for log-terminal threefolds.
We describe the set of minimal log discrepancies of toric log varities, and study its accumulation points.
We prove the existence of $n$-complements for pairs with DCC coefficients and the ACC for minimal log discrepancies of exceptional singularities. In order to prove these results, we develop the theory of complements for real coefficients.…
Minimal log discrepancies (mld's) are related not only to termination of log flips, and thus to the existence of log flips but also to the ascending chain condition (acc) of some global invariants and invariants of singularities in the Log…
We show that log canonical thresholds for complex analytic spaces satisfy the ACC.
We formulate a comparison of minimal log discrepancies of a variety and its ambient space with appropriate boundaries in terms of motivic integration. It was obtained also by Ein and Musta\c{t}\v{a} independently.
We show the validity of the Minimal Model Program for threefolds in characteristic five.