Related papers: Introduction to the log minimal model program for …

We give an alternative proof of the existence of the anticanonical minimal model program for potentially klt pairs, assuming the anticanonical divisor admits a birational Zariski decomposition. Moreover, we establish a structure theorem…

We prove that termination of lower dimensional flips for generalized klt pairs implies termination of flips for log canonical generalized pairs with a weak Zariski decomposition. Moreover, we prove that the existence of weak Zariski…

We prove that the base space of a log smooth family of log canonical pairs of log general type is of log general type as well as algebraically degenerate, when the family admits a relative good minimal model over a Zariski open subset of…

We study certain modules over the algebra of a Cartier divisor on a scheme. Using these modules, we present an inductive method for studying finite generation properties of algebras and modules. In the context of the minimal model program,…

We prove the termination of flips for 4-dimensional pseudo-effective NQC log canonical generalized pairs. As main ingredients, we verify the termination of flips for 3-dimensional NQC log canonical generalized pairs, and show that the…

We prove that many of the results of the LMMP hold for $3$-folds over fields of characteristic $p>5$ which are not necessarily perfect. In particular, the existence of flips, the cone theorem, the contraction theorem for birational extremal…

We will prove the following results for $3$-fold pairs $(X,B)$ over an algebraically closed field $k$ of characteristic $p>5$: log flips exist for $\Q$-factorial dlt pairs $(X,B)$; log minimal models exist for projective klt pairs $(X,B)$…

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 generalize the logarithmic purity theorem of Fujiwara-Kato to torsors which arise in the Kummer log flat topology under finite flat linearly reductive group schemes. As an application, we construct the logarithmic Nori fundamental group…

We prove that the pull-back of a quasi-log scheme by a smooth quasi-projective morphism has a natural quasi-log structure. We treat an application to log Fano pairs. This paper also contains a proof of the simple connectedness of log Fano…

We prove the existence of flips for $\mathbb Q$-factorial NQC generalized lc pairs, and the cone and contraction theorems for NQC generalized lc pairs. This answers a question of C. Birkar which was conjectured by J. Han and Z. Li. As an…

We provide several applications of the minimal model program to the local and global study of co-rank one foliations on threefolds. Locally, we prove a singular variant of Malgrange's theorem, a classification of terminal foliation…

For a fixed pair and fixed exponents, we prove the discreteness of log discrepancies over all log canonical triples formed by attaching a product of ideals with given exponents.

The aim of this paper is to study all the natural first steps of the minimal model program for the moduli space of stable pointed curves. We prove that they admit a modular interpretation and we study their geometric properties. As a…

In this paper, we give an affirmative answer to a conjecture in the Minimal Model Program. We prove that log $Q$-Fano varieties of dim $n$ are rationally connected. We also study the behavior of the canonical bundles under projective…

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

In this article, we introduce the logarithmic de Rham stack of a pair (X, D), for a smooth variety X over a field k of positive characteristic p, and D a strict normal crossings divisor on X. Using this stack, we prove a new version of…

We prove the Angehrn-Siu Type effective freeness and effective point separation for quasi-log canonical pairs. As a natural consequence, we obtain that these two results hold for semi-log canonical pairs. One of the main ingredients of our…

We prove a relative Kawamata Viehweg vanishing type theorem for birational morphisms. We use this to prove a Grauert Riemenschneider theorem over log canonical threefolds without zero dimensional log canonical centers, in residue…

For any quantum group of finite ADE type, we prove a new formula for the standard bilinear form evaluated at monomials. Combining this with ideas from the Lusztig-Shoji algorithm, we obtain a new algorithm that computes the canonical basis.…