Related papers: Inversion of adjunction on log canonicity

We prove sharp anti-concentration results for log-concave random variables on the real line in both the discrete and continuous setting. Our approach is elementary and uses majorization techniques to recover and extend some recent and not…

We show that the sequence of moments of order less than 1 of averages of i.i.d. positive random variables is log-concave. For moments of order at least 1, we conjecture that the sequence is log-convex and show that this holds eventually for…

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 prove a recent conjecture by Ulas on reducible polynomial substitutions.

In this short note a new proof of the monotone con- vergence theorem of Lebesgue integral on \sigma-class is given.

We prove Burkholder inequality using Bregman divergence.

We prove a conjecture of Shokurov which characterises toric varieties using log pairs.

We prove a subadjunction theorem which relates the multi-adjoint linear system of the ambient space and the linear system of the restricted bundle on a subvariety.

We introduce a new, substantially simplified version of the toggling-branching recurrence operation of Computability Logic, prove its equivalence to Japaridze's old, "canonical" version, and also prove that both versions preserve the static…

We prove that two weakened forms of Green's conjectures for canonical curves are equivalent when the genus $g$ is odd.

We prove a few cases of a conjecture on the invariance of cohomological support loci under derived equivalence by establishing a concrete connection with the related problem of the invariance of Hodge numbers. We use the main case in order…

New cases of the multiplicity conjecture are considered.

We prove Koll\'ar-type effective basepoint-free theorems for quasi-log canonical pairs.

We offer a new proof that a certain q-analogue of multinomial coeffi- cients furnishes a q-counting of the set of permutations of an associated multiset of positive integers, according to the number of inversions in such arrangements. Our…

In this paper, we study the singularities of a pair (X,Y) in arbitrary characteristic via jet schemes. For a smooth variety X in characteristic 0, Ein, Lazarsfeld and Mustata showed that there is a correspondence between irreducible closed…

We prove several extensions of the Erdos-Fuchs theorem.

We prove an equivariant version of Hironaka's theorem on elimination of points of indeterminacy. Our arguments rely on canonical resolution of singularities.

We prove the volume conjecture for any twist knots by using an equivalence relation, complex analysis, analytic continuation, and function of several complex variables on the basis of colored Jones polynomials.

We present a simpler way than usual to deduce the completeness theorem for the second-oder classical logic from the first-order one. We also extend our method to the case of second-order intuitionistic logic.

We prove an effective vanishing theorem for direct images of log pluricanonical bundles of projective semi-log canonical pairs. As an application, we obtain a semipositivity theorem for direct images of relative log pluricanonical bundles…