Related papers: Termination of (many) 4-dimensional log flips

We establish Flat Torus Theorem type results for groups acting on small cancellation complexes satisfying C(6), C(4)-T(4) and C(3)-T(6) conditions. For C(3)-T(6) complexes the result closely parallels the CAT(0) setting. For C(6) complexes…

We prove that there are finitely many families, up to isomorphism in codimension one, of elliptic Calabi-Yau manifolds $Y\rightarrow X$ with a rational section, provided that $\dim(Y)\leq 5$ and $Y$ is not of product-type. As a consequence,…

We construct exceptional Fano varieties with the smallest known minimal log discrepancies in all dimensions. These varieties are well-formed hypersurfaces in weighted projective space. Their minimal log discrepancies decay doubly…

Let $X$ be a complete algebraic variety over {\bf C}. We consider a log variety $(X,\Delta)$ that is weakly Kawamata log terminal. We assume that $K_X+\Delta$ is a {\bf Q}-Cartier {\bf Q}-divisor and that every irreducible component of…

Let X be a Fano manifold of dimension n and index n-3. Kawamata proved the non vanishing of the global sections of the fundamental divisor in the case n=4. Moreover he proved that if Y is a general element of the fundamental system then Y…

We present new explicit realizations of the most general N=4, d=1 superconformal symmetry D(2,1;\alpha) in the models of N=4 superconformal mechanics based on the reducible multiplets (1,4,3)\oplus(0,4,4), (3,4,1)\oplus(0,4,4) and…

We provide a new construction of rationality for cubic fourfolds via Mori's theory and the minimal model program. As an application, we present the solution of the Kuznetsov's conjecture for $d=42$ (the first open case). Our methods also…

Topological semantics for modal logic based on the Cantor derivative operator gives rise to derivative logics, also referred to as $d$-logics. Unlike logics based on the topological closure operator, $d$-logics have not previously been…

We prove that in any fixed dimension, K-semistable log Fano cone singularities whose volumes are bounded from below by a fixed positive number form a bounded set. As a consequence, we show that the set of local volumes of klt singularities…

In this article we define generalized pairs $(X, B+\boldsymbol{\beta})$ where $X$ is an analytic variety and $\boldsymbol{\beta}$ is a b-(1,1) current. We then prove that almost all standard results of the MMP hold in this generality for…

In this paper, we establish a vanishing theorem of Nadel type for the Witt multiplier ideals on threefolds over perfect fields of characteristic larger than five. As an application, if a projective normal threefold over $\mathbb{F}_q$ is…

We use filtered log-$\mathscr{D}$-modules to represent the (dual) localization of Saito's Mixed Hodge Modules along a smooth hypersurface, and show that they also behave well under the direct image functor and the dual functor in the…

For $g\geq2$, $j=1,\dots,g$ and $n\geq g+j$ we exhibit infinitely many new rigid and extremal effective codimension $j$ cycles in $\overline{\mathcal{M}}_{g,n}$ from the strata of quadratic differentials and projections of these strata…

We give a classification of irreducible four-dimensional symmetric spaces $G/H$ which admit compact Clifford-Klein forms, where $G$ is the transvection group of $G/H$. For this, we develop a method that applies to particular 1-connected…

This article introduces a systematic framework to understand (not to derive yet) the all-loop 4-particle amplituhedron in planar N=4 SYM, utilizing both positivity and the Mondrian diagrammatics. Its key idea is the simplest one so far: we…

Let $(X,\Delta)$ be a smooth complex projective simple normal crossing pair of dimension $n\geq 3$ endowed with an everywhere nondegenerate logarithmic conformal tensor. If $K_X+\Delta$ is not nef, then precisely one of the following…

We prove that the existence of log minimal models in dimension $d$ essentially implies the LMMP with scaling in dimension $d$. As a consequence we prove that a weak nonvanishing conjecture in dimension $d$ implies the minimal model…

In this paper we investigate boundedness and volumes of generalised pairs, and give applications to usual pairs especially to a class of pairs that we call stable log minimal models. Fixing the dimension and a DCC set controlling…

In this note, we shall prove that two smooth projective varieties of dim 2n connected by a Mukai flop have equivalent bounded derived categories. More precisely, let $\phi : X - - \to X^+$ be a Mukai flop with centers $Y \subset X$ and $Y^+…

This paper demonstrates the existence of $\mathbb{Q}$-complements for algebraically integrable log-Fano foliations on klt ambient varieties. Additionally, we investigate properties of algebraically integrable Fano foliations such as a…