Related papers: On generalized minimal log discrepancy
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.…
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 give a counterexample to the PIA (precise inversion of adjunction) conjecture for minimal log discrepancies. We also give a counterexample to the LSC conjecture for families.
We study relations between two log minimal models of a fixed lc pair. For any two log minimal models of an lc pair constructed with log MMP, we prove that there are small birational models of the log minimal models which can be connected by…
We prove that the non-vanishing conjecture holds for generalized lc pairs with a polarization.
We show that given any two minimal models of a generalized lc pair, there exist small birational models which are connected by a sequence of symmetric flops. We also present some applications.
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…
We discuss the relationship among various conjectures in the minimal model theory including the finite generation conjecture of the log canonical rings and the abundance conjecture. In particular, we show that the finite generation…
We prove the ACC for minimal log discrepancies on an arbitrary fixed threefold.
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 prove the finiteness of $B$-representations of generalised log canonical pairs. As a consequence, we prove that, the (relative) abundance for a generalised semi-log canonical pair is implied by the abundance for its normalisation.…
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 introduce linearly decomposable (LD) generalized pairs, which serve as a workable substitute for rational decompositions in the non-NQC setting. Using LD generalized pairs, together with a refinement of special termination and…
We use Koll\'ar's gluing theory to prove the contraction theorem for generalized pairs. In particular, we show that we can run the MMP for any generalized log canonical pairs.
The minimal log discrepancy is an invariant of singularities that plays an important role in the birational classification of algebraic varieties. Shokurov conjectured that the minimal log discrepancy can always be bounded from above in…
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.
Under the assumption of the minimal model theory for projective klt pairs of dimension $n$, we establish the minimal model theory for lc pairs $(X/Z,\Delta)$ such that the log canonical divisor is relatively log abundant and its restriction…
We prove the special termination for log canonical pairs and its generalisation in the context of generalised pairs.
We prove the existence of flips for $\mathbb Q$-factorial NQC generalized lc pairs, and the cone and contraction theorems for NQC generalized lc pairs. This answers a question of C. Birkar which was conjectured by J. Han and Z. Li. As an…