Related papers: Inversion of adjunction on log canonicity

We combinatorially prove that the number $R(n,k)$ of permutations of length $n$ having $k$ runs is a log-concave sequence in $k$, for all $n$. We also give a new combinatorial proof for the log-concavity of the Eulerian numbers.

In this note, we establish a generalized analytic inversion of adjunction via the Nadel-Ohsawa multiplier/adjoint ideal sheaves associated to plurisubharmonic (psh) functions for log pairs, by which we answer a question of Koll\'{a}r in…

We prove the reverse ultra log-concavity of the Boros-Moll polynomials. We further establish an inequality which implies the log-concavity of the sequence $\{i!d_i(m)\}$ for any $m\geq 2$, where $d_i(m)$ are the coefficients of the…

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.

We prove the ideal-adic semi-continuity of minimal log discrepancies on surfaces.

A vector variational principle is proved.

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 give a new proof of Lucas' Theorem in elementary number theory.

The postulates of comprehension and extensionality in set theory are based on an inversion principle connecting set-theoretic abstraction and the property of having a member. An exactly analogous inversion principle connects functional…

We propose a variant of the effective adjunction conjecture for lc-trivial fibrations. This variant is suitable for inductions and can be used to treat real coefficients.

The paper presents a counterexample to the Hodge conjecture.

We show that the Jacobian conjecture of the two dimensional case is true.

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,…

We prove the finite generation of the adjoint ring for $\mathbb{Q}$-factorial log surfaces over any algebraically closed field.

A simple proof is given for the convexity of log det (I+K X^{-1}) in the positive definite matrix variable X with a given positive semidefinite K.

We generalize the injectivity theorem of Esnault and Viehweg, and apply it to the structure of log canonical type divisors.

We prove a counterpart of the log-convex density conjecture in the hyperbolic plane.

We show that the description of Deligne--Beilinson cohomology is improved by using log Hodge theory. We consider the log relative version of it, and also present a fundamental conjecture in log Hodge theory.

In this note we obtain a new convergence result for the Adomian decomposition method.

We propose a detailed proof of the fact that the inverse of Ackermann function is computable in linear time.