Related papers: Remarks on log pluricanonical representations

We prove the abundance theorem for numerically trivial log canonical divisors of log canonical pairs and semi-log canonical pairs.

For families of continuous plurisubharmonic functions we show that, in a local sense, separately bounded above implies bounded above.

In this paper, we generalise the theory of complements to log canonical log fano varieties and prove boundedness of complements for them in dimension less than or equal to 3. We also prove some boundedness results for the canonical index of…

We give a broad survey of inequalities for the number of linear extensions of finite posets. We review many examples, discuss open problems, and present recent results on the subject. We emphasize the bounds, the equality conditions of the…

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

Several structural properties of a universal algebra can be seen from the higher commutators of its congruences. Even on a finite algebra, the sequence of higher commutator operations is an infinite object. In the present paper, we exhibit…

This paper shows that Mustata-Nakamura's conjecture holds for pairs consisting of a smooth surface and a multiideal with a real exponent over the base field of positive characteristic. As corollaries, we obtain the ascending chain condition…

In this paper, we prove a minimal modularity lifting theorem for Galois representations (conjecturally) associated to Siegel modular forms of genus two which are holomorphic limits of discrete series at infinity.

Here we deal with the logic of [GuSh 533], which tries to capture polynomial time (for finite models). There it is proved that the logic cannot say much on models with equality only. Here we prove that it cannot say much on models for which…

This paper is about the logarithmic limit sets of real semi-algebraic sets, and, more generally, about the logarithmic limit sets of sets definable in an o-minimal, polynomially bounded structure. We prove that most of the properties of the…

We prove a lower bound on the canonical height associated to polynomials over number fields evaluated at points with infinite forward orbit. The lower bound depends only on the degree of the polynomial, the degree of the number field, and…

We prove the ascending chain condition for log canonical thresholds of bounded coregularity.

We prove that for any weakly convergent sequence of finite graphs with bounded vertex degrees, there exists a topological limit graphing.

We give a criterion when a polynomial $x^n-g$ is irreducible over a pseudofinite field. As an application we give an explicit description of algebraic closure of some pseudofinite fields of zero characteristic.

We prove two completeness results, one for the extension of dependence logic by a monotone generalized quantifier Q with weak interpretation, weak in the meaning that the interpretation of Q varies with the structures. The second result…

We formulate and prove finite dimensional analogs for the classical Balian-Low theorem, and for a quantitative Balian-Low type theorem that, in the case of the real line, we obtained in a previous work. Moreover, we show that these results…

We provides some useful estimates for solving martingale representation problem under G-expectations. We also study the corresponding conditions for the existence and uniqueness.

Let $K$ be an unramified $p$-adic local field and let $W$ be the ring of integers of $K$. Let $(X,S)/W$ be a smooth proper scheme together with a simple normal crossings divisor and fix positive integers $r$ and $f$. We show that the set of…

We prove an analogue of the celebrated Hall-Higman theorem, which gives a lower bound for the degree of the minimal polynomial of any semisimple element of prime power order $p^{a}$ of a finite classical group in any nontrivial irreducible…

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