Related papers: On generalized minimal log discrepancy

We describe the foundation of the log minimal model program for log canonical pairs according to Ambro's idea. We generalize Koll\'ar's vanishing and torsion-free theorems for embedded simple normal crossing pairs. Then we prove the cone…

We establish the minimal model theory for normal pairs along log canonical locus in the complex analytic setting. This is the complex analytic analog of the previous result by the author.

The main purpose of this paper is to establish some useful partial resolutions of singularities for pairs from the minimal model theoretic viewpoint. We first establish the existence of log canonical modifications of normal pairs under some…

We discuss a difference between the rational and the real non-vanishing conjecture for pseudo-effective log canonical divisors of log canonical pairs. We also show the log non-vanishing theorem for rationally connected varieties under…

We discuss the relative log minimal model theory for log surfaces in the analytic setting. More precisely, we show that the minimal model program, the abundance theorem, and the finite generation of log canonical rings hold for log pairs of…

We prove that the union-closed sets conjecture is true for separating union-closed families $\mathcal{A}$ with $|\mathcal{A}| \leq 2\left(m+\frac{m}{\log_2(m)-\log_2\log_2(m)}\right)$ where $m$ denotes the number of elements in…

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.

The nonvanishing conjecture for projective log canonical pairs plays a key role in the minimal model program of higher dimensional algebraic geometry. The numerical nonvanishing conjecture considered in this paper is a weaker version of the…

We study the behavior of generalized lc pairs with $\mathrm{\textbf b}$-log abundant nef part, a meticulously designed structure on algebraic varieties. We show that this structure is preserved under the canonical bundle formula and…

We show that minimal models of log canonical pairs exist, assuming the existence of minimal models of smooth varieties.

We compare the minimal model of a log canonical pair with the minimal model of its reduced boundary. These results are then used to study the existence of the minimal model of a semi-log-canonical pair using its normalization.

A generic computation of a subset A of the natural numbers consists of a a computation that correctly computes most of the bits of A, and which never incorrectly computes any bits of A, but which does not necessarily give an answer for…

We describe the set of minimal log discrepancies of toric log varities, and study its accumulation points.

We survey the known and expected properties of the minimal log discrepancy, the local invariant of a log variety.

We establish a relative spannedness for log canonical pairs, which is a generalization of the basepoint-freeness for varieties with log-terminal singularities by Andreatta--Wi\'sniewski. Moreover, we establish a generalization for quasi-log…

We obtain a correct generalization of Shokurov's non-vanishing theorem for log canonical pairs. It implies the base point free theorem for log canonical pairs. We also prove the rationality theorem for log canonical pairs. As a corollary,…

This paper shows that Mustata-Nakamura's conjecture holds for pairs consisting of a smooth surface and a multiideal with a real exponent over the base field of positive characteristic. As corollaries, we obtain the ascending chain condition…

We formulate a generalization of Vojta's conjecture in terms of log pairs and variants of multiplier ideals. In this generalization, a variety is allowed to have singularities. It turns out that the generalized conjecture for a log pair is…

We show the semi-continuity property of minimal log discrepancies for varieties which have a crepant resolution in the category of Deligne-Mumford stacks. Using this property, we also prove the ideal-adic semi-continuity problem for toric…

We show that generalized log canonical thresholds for complex analytic spaces satisfy the ACC and we characterize the accumulation points.