Related papers: Balanced line bundles on Fano varieties
We verify Katzarkov-Kontsevich-Pantev conjecture for Landau-Ginzburg models of smooth Fano threefolds.
In this paper, we give a partial affirmative answer to the BAB conjecture for $3$-folds in characteristic $p>5$. Specifically, we prove that a set $\mathcal{D}$ of weak Fano $3$-folds over an uncountable algebraically closed field is…
We construct canonical heights of subvarieties for dynamical system of several morphisms associated with line bundles defined over a number field, and study some of their properties. We also construct invariant currents for such systems…
In this paper, we advance the classification of toric 2-Fano manifolds by continuing the investigation of the minimal projective bundle dimension $m(X) \in \{1,\dots,\dim(X)\}$ introduced in our previous work. This invariant captures the…
This paper is devoted to the study of holomorphic distributions of dimension and codimension one on smooth weighted projective complete intersection Fano manifolds threedimensional, with Picard number equal to one. We study the relations…
We describe limits of line bundles on nodal curves in terms of toric arrangements associated to Voronoi tilings of Euclidean spaces. These tilings encode information on the relationship between the possibly infinitely many limits, and…
We introduce the notion of an instanton bundle on a Fano threefold of index 2. For such bundles we give an analogue of a monadic description and discuss the curve of jumping lines. The cases of threefolds of degree 5 and 4 are considered in…
We study quotients of multi-graded bundles, including double vector bundles. Among other things, we show that any such quotient fits into a tower of affine bundles. Applications of the theory include a construction of normal bundles for…
We study Fano threefolds with~terminal singularities admitting a "minimal" action of a finite group. We prove that under certain additional assumptions such a variety does not contain planes. We also obtain an upper bounds of the number of…
In this book, we establish a theory of adelic line bundles over quasi-projective varieties over finitely generated fields. Besides definitions of adelic line bundles, we consider their intersection theory, volume theory, and height theory,…
In this paper, we show an extension type theorem for twisted pluricanonical sections on a family of smooth projective manifolds (the twisting line bundle being pseudo-effective and having a prescribed multiplier ideal on the central fiber).
It is known that there are only finitely many mutation-equivalence classes with a given singularity content, and each of these equivalence classes contains only finitely many minimal polygons. We describe an efficient algorithm to classify…
We discuss various results on Hilbert schemes of lines and conics and automorphism groups of smooth Fano threefolds with Picard rank 1. Besides a general review of facts well known to experts, the paper contains some new results, for…
We prove that the Fano variety of lines of a generic cubic fourfold containing a plane is isomorphic to a moduli space of twisted stable complexes on a K3 surface. On the other hand, we show that the Fano varieties are always birational to…
We find a characterization for Fano 4-folds $X$ with Lefschetz defect $\delta_{X}=3$: besides the product of two del Pezzo surfaces, they correspond to varieties admitting a conic bundle structure $f\colon X\to Y$ with…
We compute global log canonical thresholds, or equivalently alpha invariants, of birationally rigid orbifold Fano threefolds embedded in weighted projective spaces as codimension two or three. As an important application, we prove that most…
This paper deals with some basic constructions of linear and multilinear algebra on finite-dimensional diffeological vector spaces. We consider the diffeological dual formally checking that the assignment to each space of its dual defines a…
We prove that a smooth complex projective threefold with a K\"ahler metric of negative holomorphic sectional curvature has ample canonical line bundle. In dimensions greater than three, we prove that, under equal assumptions, the nef…
Given a covering f: X \to Y of projective manifolds, we consider the vector bundle E on Y given as the dual of f_*(\O_X) / \O_Y. This vector bundles often has positivity properties, e.g. E is ample when Y is projective space by a theorem of…
In this paper, we consider the CM line bundle on the K-moduli space, i.e., the moduli space parametrizing K-polystable Fano varieties. We prove it is ample on any proper subspace parametrizing reduced uniformly K-stable Fano varieties which…