Related papers: On log canonical inversion of adjunction

The aim of the paper is to characterize Kawamata log terminal singularities and log canonical singularities by dimensions of jet schemes. It is a generalization of Mustata's result.

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.

In this paper we show that the set of accumulation points of generalized log canonical thresholds for certain DCC sets comes from the set of generalized log canonical thresholds of dimension $1$ less of the same DCC sets.

We prove that the local accumulation complexity of the set of log canonical volumes in dimension $\geq 2$ can be infinite.

We prove Fujita-type basepoint-freeness for projective quasi-log canonical curves and surfaces.

Let $(X,B)$ be a log canonical pair over a normal variety $Z$ with maximal Albanese dimension. If $K_X+B$ is relatively abundant over $Z$ (for example, $K_X+B$ is relatively big over $Z$), then we prove that $K_X+B$ is abundant. In…

We study the compositional inverses of some general classes of permutation polynomials over finite fields. We show that we can write these inverses in terms of the inverses of two other polynomials bijecting subspaces of the finite field,…

Using the local bijectivity of Keller maps, we give a proof of two-dimensional Jacobian conjecture.

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

We generalize Demailly's construction of projective jet bundles and strictly negatively curved pseudometrics on them to the logarithmic case. We establish this logarithmic generalization explicitly via coordinates, just as Noguchi's…

We prove the Nonvanishing conjecture for uniruled projective log canonical pairs of dimension $n$, assuming the Nonvanishing conjecture for smooth projective varieties in dimension $n-1$. We also show that the existence of good minimal…

In this work we present an analogue of the inverse scattering for Canonical systems using theory of vessels and associated to them completely integrable systems. Analytic coefficients fits into this setting, significantly expanding the…

We reformulate base point free theorems. Our formulation is flexible and has some important applications. One of the main purposes of this paper is to prove a generalization of the base point free theorem in Fukuda's paper: On numerically…

We prove analogues of fundamental results of Kostant on the universal centralizer of a connected reductive algebraic group for algebraically closed fields of positive characteristic (with mild assumptions), and for integral coefficients. As…

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.

In this paper we study the question asked by Caucher Birkar about injectivity theorem on cohomologies of generalised pairs. By applying techniques from complex analytic geometry, we show that the injectivity theorem holds for generalised…

The main purpose of the following article is to give a proof of Y. Kawamata's celebrated subadjunction theorem in the spirit of our previous work on Bergman kernels. We will use two main ingredients : an $\displaystyle L^{2\over…

For every smooth complex projective variety $W$ of dimension $d$ and nonnegative Kodaira dimension, we show the existence of a universal constant $m$ depending only on $d$ and two natural invariants of the very general fibres of an Iitaka…

We prove Union-Closed sets conjecture.

We verify that the descent maps provided by Langlands's Conjugacy Conjecture do satisfy the continuity condition necessary for them to be effective. Thus Langlands's conjecture does imply the existence of canonical models. This replaces an…