Related papers: Effective base point free theorem for log canonica…

In this article we show that the Log Minimal Model Program for $\mathbb{Q}$-factorial dlt pairs $(X, B)$ on a compact K\"ahler $3$-fold holds. More specifically, we show that after finitely many divisorial contractions and flips we obtain…

We give algorithms of computing bases of logarithmic cohomology groups for square-free polynomials in two variables. (Fixed typos of v1)

We give a counting based proof of the Graham Pollak Theorem

Let $(X, \Delta)/U$ be klt pairs and $Q$ be a convex set of divisors. Assuming that the relative Kodaira dimensions are non-negative, then there are only finitely many log canonical models when the boundary divisors varying in a relatively…

The canonical transformation and its unitary counterpart which relate the rational Calogero-Moser system to the free one are constructed.

We prove that the log canonical thresholds of a large class of binomial ideals, such as complete intersection binomial ideals and the defining ideals of space monomial curves, are computable by linear programming.

We define a canonical quadratic pair on the Clifford algebra of an algebra with quadratic pair over a field. This allows us to extend to the characteristic 2 case the notion of trialitarian triples, from which we derive a characterization…

Let $k$ be an $F$-finite field containing an infinite perfect field of positive characteristic. Let $(X, \Delta)$ be a projective log canonical pair over $k$. In this note we show that, for a semi-ample divisor $D$ on $X$, there exists an…

We prove the existence of good log minimal models for dlt pairs of numerical log Kodaira dimension 0.

We prove a analog of Kurosh theorem for countable Borel equivalence relations giving the structure of sub-relations in free products.

Under the assumption of the minimal model theory for projective klt pairs of dimension $n$, we establish the minimal model theory for lc pairs $(X/Z,\Delta)$ such that the log canonical divisor is relatively log abundant and its restriction…

The nonvanishing conjecture for projective log canonical pairs plays a key role in the minimal model program of higher dimensional algebraic geometry. The numerical nonvanishing conjecture considered in this paper is a weaker version of the…

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 show that the existence of a birational weak Zariski decomposition for a pseudo-effective generalized polarized lc pair is equivalent to the existence of a generalized polarized log terminal model.

We generalize the formula for the log canonical threshold(LCT) of plane curves over the complex numbers to arbitrary characteristics. Our proof relies purely on valuation theory, instead of on the theory of $D$-modules.

We prove that integral points can be effectively determined on all but finitely many modular curves, and on all but one modular curve of prime power level.

We compute the class of the closure of the locus of canonical divisors in the projectivization of the Hodge bundle $\mathbb{P}\overline{\mathcal{H}}_g$ over $\overline{\mathcal{M}}_g$ which have a zero at a Weierstrass point. We also show…

We prove the decidability of the elementary theory of a free group.

We construct pairs of algebras with mixed independence relations by using truncations of reduced free products of algebras. For example, we construct free-Boolean pairs of algebras and free-monotone pairs of algebras. We also introduce…

We prove formulas for the core of ideals that apply in arbitrary characteristic.