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

In this paper we give an elementary proof of the Zariski-Lipman conjecture for log canonical spaces.

We consider the Zariski-Lipman Conjecture on free module of derivations for algebraic surfaces. Using the theory of non-complete algebraic surfaces, and some basic results about ruled surfaces, we will prove the conjecture for several…

We prove the special termination for log canonical pairs and its generalisation in the context of generalised pairs.

Let $X$ be a normal variety. Assume that for some reduced divisor $D \subset X$, logarithmic 1-forms defined on the snc locus of $(X, D)$ extend to a log resolution $\tilde X \to X$ as logarithmic differential forms. We prove that then the…

We study the failure of the Lipman-Zariski conjecture in positive characteristic. For rational double points, the conjecture holds true except for a short finite list of exceptions. For log canonical surface singularities, the conjecture…

We prove inversion of adjunction on log canonicity.

We prove the Invariant Subspace Conjecture for separable Hilbert spaces.

We give a short proof of the Zariski-Lipman conjecture for toric varieties: any complex toric variety with locally free tangent sheaf is smooth.

We prove two theorems on the locally finite decompositions of the cones of divisors by the cones which correspond to canonical and minimal models. We introduce the concept of the numerical linear systems in order to simplify the argument on…

We propose a subconjecture that implies the semiampleness conjecture for quasi-numerically positive log canonical divisors and prove the semiampleness in some elementary cases.

We consider a version of the Lipman-Zariski conjecture for logarithmic vector fields and logarithmic $1$-forms on pairs. Let $(X,D)$ be a pair consisting of a normal complex variety $X$ and an effective Weil divisor $D$ such that the sheaf…

We prove that the non-vanishing conjecture holds for generalized lc pairs with a polarization.

We give counterexamples to Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients.

We prove the termination of flips for 4-dimensional pseudo-effective NQC log canonical generalized pairs. As main ingredients, we verify the termination of flips for 3-dimensional NQC log canonical generalized pairs, and show that the…

We prove Koll\'ar's effective base point free theorem for log canonical pairs.

We show that log canonical thresholds for complex analytic spaces satisfy the ACC.

We prove the Jacobian Conjecture for the space of all the inner functions in the unit disc.

We show some inductive statements for the index conjecture for log canonical Calabi-Yau pairs. Using it, we show that boundedness of log canonical index for log canonical Calabi Yau pairs with rational DCC coefficients in dimension 3. We…

The present paper is concerned with differential forms on log canonical varieties. It is shown that any p-form defined on the smooth locus of a variety with canonical or klt singularities extends regularly to any resolution of…

We prove a result on the inversion of adjunction for log canonical pairs that generalizes Kawakita's result to log canonical centers of arbitrary codimension.