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

We give a new proof of the finiteness of B-representations. As a consequence of the finiteness of B-representations and Koll\'ar's gluing theory on lc centers, we prove that the (relative) abundance conjecture for slc pairs is implied by…

We give an example of a finite rank, in fact aleph-1 categorical theory where the CBP (canonical base property) does not hold. We include a "group-like" example. We also prove, in a finite Morley rank context, if all definable Galois groups…

We prove the Cone Theorem for algebraically integrable foliations. As a consequence, we show that termination of flips implies the b-nefness of the moduli part of a log canonical pair with respect to a contraction, generalising the case of…

We prove the finiteness of log pluricanonical representations for projective log canonical pairs with semi-ample log canonical divisor. As a corollary, we obtain that the log canonical divisor of a projective semi log canonical pair is…

Kang, Kashiwara, Kim and Oh have proved that cluster monomials lie in the dual canonical basis, under a symmetric type assumption. This involves constructing a monoidal categorification of a quantum cluster algebra using representations of…

Kolmogorov's invariant torus theorem is proved using a simple fixed point theorem.

We proved a KAM theorem on existence of invariant tori in generalized Hamiltonian systems without action-angle variables. It is a generalization of the result of de la Llave et al. [Llave, 2005] that deals with canonical Hamiltonian system.

We discuss the relationship among various conjectures in the minimal model theory including the finite generation conjecture of the log canonical rings and the abundance conjecture. In particular, we show that the finite generation…

We prove a generic Torelli theorem for a class of three-dimensional log Calabi--Yau pairs $(Y, D)$ with maximal boundary.

In this paper, we prove the non-vanishing and some special cases of the abundance for log canonical threefold pairs over an algebraically closed field $k$ of characteristic $p > 3$. More precisely, we prove that if $(X,B)$ be a projective…

In this article we give a Galois-theoretic characterization of the canonical theta structure. The Galois property of the canonical theta structure translates into certain $p$-adic theta relations which are satisfied by the canonical theta…

This paper investigates the logical strength of completeness theorems for modal propositional logic within second-order arithmetic. We demonstrate that the weak completeness theorem for modal propositional logic is provable in…

The aim of this article is to give a new proof of Cohen-Gabber theorem in the equal characteristic $p>0$ case.

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 exhibit a uniform method for obtaining (wellfounded and non-wellfounded) cut-free sequent-style proof systems that are sound and complete for various classes of action algebras, i.e., Kleene algebras enriched with meets and residuals.…

We prove divisibility results for the Fourier coefficients of canonical basis elements for the spaces of weakly holomorphic modular forms of weight $0$ and levels $6, 10, 12, 18$ with poles only at the cusp at infinity. In addition, we show…

We generalize Koll\'ar's conjecture (including torsion freeness, injectivity theorem, vanishing theorem and decomposition theorem) to Saito's $S$-sheaves twisted by a $\mathbb{Q}$-divisor. This gives a uniform treatment for various kinds of…

In this paper, we construct a canonical linear basis for free commutative integro-differential algebras by applying the method of Gr\"obner-Shirshov bases. We establish the Composition-Diamond Lemma for free commutative differential…

We generalize several recognizability theorems for free single-sorted algebras to the field of many-sorted algebras and provide, in a uniform way and without using neither regular tree grammars nor tree automata, purely algebraic proofs of…

In this paper, we establish a basepoint free theorem of Angehrn-Siu type in positive characteristic. Moreover, we also give an effective bound for very ampleness in arbitrary characteristic.