相关论文: Effective base point free theorem for log canonica…

We prove inversion of adjunction on log canonicity.

We show that the log canonical threshold polytopes of varieties with log canonical singularities satisfy the ascending chain condition.

For the quantum symmetric pair $(\textbf{U}, \textbf{U}^{\imath})$ of type AIII/AIV, we show various positivity properties of the $\imath$-canonical bases on finite-dimensional simple $\textbf{U}$-modules, as well as their tensor product.

We prove that if $(X, B+\mathbf{M})$ is a generalized klt pair with $K_X+B+\mathbf{M}_X$ nef and abundant, then $K_X+B+\mathbf{M}_X$ is semiample. More generally, we prove a generalized basepoint free theorem for generalized klt pairs.

In this paper, we show that Fujita's basepoint-freeness conjecture for projective quasi-log canonical singularities holds true in dimension three. Immediately, we prove Fujita-type basepoint-freeness for projective semi-log canonical…

We prove that the log canonical ring of a projective log canonical pair in Kodaira dimension two is finitely generated.

A unipotent triangular relationship is established between the dual standard monomial theoretic basis and canonical basis for the negative part of the quantized universal enveloping algebra of type A.

We describe how Computational Group Theory provides tools for manipulating tensors in explicit index notation. In special, we present an algorithm that puts tensors with free indices obeying permutation symmetries into the canonical form.…

We give explicit atomic bases of arbitrary coefficient-free cluster algebras of types $A$ and $\widetilde A$.

Prokhorov and Shokurov introduced the famous effective adjunction conjecture, also known as the effective base-point-freeness conjecture. This conjecture asserts that the moduli component of an lc-trivial fibration is effectively…

We prove the existence of $n$-complements for pairs with DCC coefficients and the ACC for minimal log discrepancies of exceptional singularities. In order to prove these results, we develop the theory of complements for real coefficients.…

We consider pairs (X,A), where X is a variety with klt singularities and A is a formal product of ideals on X with exponents in a fixed set that satisfies the Descending Chain Condition. We also assume that X has (formally) bounded…

We show that the Lie's Theorem holds for Lie color algebras with a torsion-free abelian group $G$. We give an example to show that the torsion-free condition is necessary.

We offer a direct proof of an elementary result concerning cohomological periods. As a corollary we show that given a finitely generated stably free resolution of Z over a finite group, two of its modules are free.

We examine the Sobolev space associated with the linear canonical Dunkl transform and explore some properties of the linear canonical Dunkl operators. Building on these results, we establish a real Paley-Wiener theorem for the linear…

We formulate and prove a free quantum analogue of the first fundamental theorems of invariant theory. More precisely, the polynomial functions algebras are replaced by free algebras, while the universal cosovereign Hopf algebras play the…

We derive a straightening-free algorithm that computes the canonical bases of any higher-level q-deformed Fock space.

We propose the notion of a coarse cohomology theory and study the examples of coarse ordinary cohomology, coarse stable cohomotopy and of coarse cohomology theories obtained by dualizing coarse homology theories. We show that the dualizing…

We show that the family of semi log canonical pairs with ample log canonical class and with fixed volume is bounded.

In this paper, we introduce a new type of coupled fixed point theorem in partially ordered complete metric space. We give an example to support of our result.