Related papers: Minimal model program for algebraically integrable…

Given a canonical algebraically integrable foliation on a klt projective variety, we study the variation of the ample models of the associated adjoint foliated structures with respect to the parameter. When the foliation is of general type,…

We use reduction maps to study the minimal model program. Our main result is that the existence of a good minimal model for a klt pair $(X,\Delta)$ can be detected on the base of the $(K_{X}+\Delta)$-trivial reduction map. Thus we show that…

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…

We establish the minimal model theory for normal pairs along log canonical locus in the complex analytic setting. This is the complex analytic analog of the previous result by the author.

We establish the Minimal Model Program for arithmetic threefolds whose residue characteristics are greater than five. In doing this, we generalize the theory of global $F$-regularity to mixed characteristic and identify certain stable…

Let $f: X \to Z$ be a fibration from a normal projective variety $X$ of dimension $n$ onto a normal curve $Z$ over a perfect field of characteristic $p>2$. Let $(X, B)$ be a dlt pair such that the induced pair on a general fibre is log…

We consider a canonical bundle formula for generically finite proper surjective morphisms and obtain subadjunction formulae for minimal log canonical centers of log canonical pairs. We also treat related topics and applications.

We determine all values of the parameters for which the cell modules form a standard system, for a class of cellular diagram algebras including partition, Brauer, walled Brauer, Temperley-Lieb and Jones algebras. For this, we develop and…

We establish the minimal model program for log canonical and Q-factorial surfaces over excellent base schemes.

In the present paper we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free group and introduce three axioms for the corresponding…

We use the theory of foliations to study the relative canonical divisor of a normalized inseparable base-change. Our main technical theorem states that it is linearly equivalent to a divisor with positive integer coefficients divisible by…

We discuss the relative log minimal model theory for log surfaces in the analytic setting. More precisely, we show that the minimal model program, the abundance theorem, and the finite generation of log canonical rings hold for log pairs of…

We consider the integrable XXZ model with the special open boundary conditions. We perform Quantum Group reduction of this model in roots of unity and use it for the definition Minimal Models of Interable lattice theory. It is shown that…

Given a minuscule representation of a simple Lie algebra, we find an algebraic model for the action of a regular element and show that these models can be glued together over the adjoint quotient, viewed as the set of all regular conjugacy…

We study very basic slc-trivial fibrations. We show that restricting on any lc center of a very basic slc-trivial fibration, its moduli part is numerically trivial if and only if it is $\mathbb Q$-linearly trivial. We then prove that…

We prove existence of flips, special termination, the base point free theorem and, in the case of log general type, the existence of minimal models for F-dlt foliated pairs of co-rank one on a $\mathbb Q$-factorial projective threefold. As…

We prove that one can run the log minimal model program for log canonical $3$-fold pairs in characteristic $p>5$. In particular we prove the Cone Theorem, Contraction Theorem, the existence of flips and the existence of log minimal models…

Frame bundles equipped with a principal connection have their local structure characterised by a 1-form, called the Cartan connection 1-form, which gathers the principal connection form and the soldering form. We introduce generalised frame…

We study the termination of minimal model programs for log canonical pairs in the complex analytic setting. By using the termination, we prove a relation between the minimal model theory for projective log canonical pairs and that for log…

We introduce the notion of generalized MR log canonical surfaces and establish the minimal model theory for generalized MR log canonical surfaces in full generality.