Related papers: On log canonical rings

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

We prove that the ACC conjecture for minimal log discrepancies holds for threefolds in $[1-\delta,+\infty)$, where $\delta>0$ only depends on the coefficient set. We also study Reid's general elephant for pairs, and show Shokurov's…

On smooth threefolds, the ACC for minimal log discrepancies is equivalent to the boundedness of the log discrepancy of some divisor which computes the minimal log discrepancy. We reduce it to the case when the boundary is the product of a…

The log-rank conjecture is one of the fundamental open problems in communication complexity. It speculates that the deterministic communication complexity of any two-party function is equal to the log of the rank of its associated matrix,…

Using the Rowland idea, we find two infinite sets of generators of primes. We also pose some conjectures concerning twin primes.

Let $d(G)$ be the smallest cardinality of a generating set of a finite group $G.$ We give a complete classification of the finite groups with the property that, whenever $ \langle x_1, \dots, x_{d(G)} \rangle = \langle y_1, \dots, y_{d(G)}…

We use Koll\'ar's gluing theory to prove the contraction theorem for generalized pairs. In particular, we show that we can run the MMP for any generalized log canonical pairs.

In this paper, we show that the minimal model theory does not hold in characteristic two. More precisely, we construct counter-examples to the relative abundance conjecture.

We prove that the log Iitaka conjecture holds for log canonical fibrations when log canonical divisor of a sufficiently general fiber is abundant.

Using a new technique, we prove a rich family of special cases of the matroid intersection conjecture. Roughly, we prove the conjecture for pairs of tame matroids which have a common decomposition by 2-separations into finite parts.

We give a reformulation of the Lehmer conjecture about algebraic integers in terms of a simple counting problem modulo p.

We announce a number of conjectures associated with and arising from a study of primes and irrationals in $\mathbb{R}$. All are supported by numerical verification to the extent possible.

We prove that a log surface has only finitely many weakly log canonical projective models with klt singularities up to log isomorphism, by reducing the problem to the boundedness of their polarization.

In this paper we provide a complete algebraic characterization of elementary equivalence of rings with a finitely generated additive group in the language of pure rings. The rings considered are arbitrary otherwise.

The $MLS$ conjecture states that every finite simple group has a minimal logarithmic signature. The aim of this paper is proving the existence of a minimal logarithmic signature for some simple unitary groups $PSU_{n}(q)$. We report a gap…

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

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…

We establish a relative spannedness for log canonical pairs, which is a generalization of the basepoint-freeness for varieties with log-terminal singularities by Andreatta--Wi\'sniewski. Moreover, we establish a generalization for quasi-log…

We formulate a generalization of Vojta's conjecture in terms of log pairs and variants of multiplier ideals. In this generalization, a variety is allowed to have singularities. It turns out that the generalized conjecture for a log pair is…

We discuss the minimal model program for b-log varieties, which is a pair of a variety and a b-divisor, as a natural generalization of the minimal model program for ordinary log varieties. We show that the main theorems of the log MMP work…