相关论文: The Zariski-Lipman conjecture for log canonical sp…

We present a new uniform method for studying modal companions of superintuitionistic rule systems and related notions, based on the machinery of stable canonical rules. Using this method, we obtain alternative proofs of the Blok-Esakia…

We prove that the non-vanishing conjecture and the log minimal model conjecture for projective log canonical pairs can be reduced to the non-vanishing conjecture for smooth projective varieties such that the boundary divisor is zero.

In this paper we give an elementary proof of the local sum conjecture in two dimensions. In a remarkable paper [CMN, arXiv:1810.11340], this conjecture has been established in all dimensions using sophisticated, powerful techniques from a…

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

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…

In this note we prove the Weinstein conjecture for a class of symplectic manifolds including the uniruled manifolds based on Liu-Tian's result.

We prove that the Bourgain slicing conjecture and the Kannan-Lov\'asz-Simonovits (KLS) isoperimetric conjecture in $\mathbb{R}^n$ hold true up to a factor of $\sqrt{\log n}$. A new ingredient used in the proof is an improved log-concave…

Given an ambient variety $X$ and a fixed subvariety $Z$ we give sufficient conditions for the existence of a boundary $\Delta$ such that $Z$ is a log canonical center for the pair $(X, \Delta)$. We also show that under some additional…

We prove a flat strip theorem for 2-dimensional ptolemaic spaces.

In this note, we give some new families of two-stage spaces for which the torus rank conjecture is affirmed.

We develop a new method to deal with the Cancellation Conjecture of Zariski in different environments. We prove the conjecture for free associative algebras of rank two. We also produce a new proof of the conjecture for polynomial algebras…

We show the finiteness of log pluricanonical representations under the assumption of the existence of a good minimal model.

In this article, we give a proof on the Arnold-Chekanov Lagrangian intersection conjecture on the cotangent bundles and its generalizations.

We obtain a system of relations between linear Hodge integrals. As an application, we show that its first non-trivial relation implies the Witten's Conjecture/Kontsevich Theorem.

This is a survey on Sarnak's Conjecture

We prove the existence of log canonical modifications for a log pair. As an application, together with Koll\"ar's gluing theory, we remove the assumption in the first named author's work [Odaka11], which shows that K-semistable polarized…

In this paper we prove a generalization of famous Larchr's theorem concerning good lattice points.

The moduli space of jets of certain G-structures (basically those which admit a canonical linear connection) is shown to be isomorphic to the quotient of a natural G-module by G.

An alternative proof of the duality of generalized Lie bialgebroid is given and proved a canonical Jacobi structure can be defined on the base of it. We also introduce the notion of morphism between generalized Lie bialgebroids and proved…

We prove a conjecture stated in a previous paper by the author about the existence of canonical filtrations for a family of vertex operator algebras in rational levels.