Related papers: Partially ample line bundles and base loci
Motivated by conjectures of Demailly, Green-Griffiths, Lang, and Vojta, we show that several notions related to hyperbolicity behave similarly in families. We apply our results to show the persistence of arithmetic hyperbolicity along field…
We study smooth projective complex varieties with ample cotangent bundle. Our main result is that in an abelian variety of dimension n, a complete intersection of at least n/2 general hypersurfaces of sufficiently high degrees has ample…
Generalized are the investigated in other works of the author transports along paths in fibre bundles to transports along arbitrary maps in them. Their structure and some properties are studied. Special attention is paid to the linear case…
In this article we give several examples of line bundles on certain non-compact surfaces that cannot be equipped with a flat connection.
Given a line bundle L on a smooth projective curve over the complex numbers, we show that a general extension E of L by the trivial line bundle is very stable: line bundles contained in E have degree much less than half the degree of E.…
A ribbon is a first-order thickening of a non-singular curve. Motivated by a question of Eisenbud and Green, we show that a compactification of the moduli space of line bundles on a ribbon is given by the moduli space of semi-stable…
In this paper, extending the recent work of authors with Calles Loperena and Dimitrijevi\'c Blagojevi\'c, we give a general and complete treatment of a problem of partition of mass assignments with prescribed arrangements of hyperplanes on…
In this paper, we studied the map defined by a non-very ample line bundle on some special irregular varieties. As to this topic, it is well known that for a line bundle $L$ on an Abelian variety $A$, the linear system $|2L|$ is base point…
Our interest is a regularity of a minimal singular metric of a line bundle. One main conclusion of our general result in this paper is the existence of continuous Hermitian metrics with semi-positive curvatures on the so-called Zariski's…
By [R. Bautista, P. Gabriel, A.V Roiter., L. Salmeron, Representation-finite algebras and multiplicative basis. Invent. Math. 81 (1985) 217-285.], a finite-dimensional algebra having finitely many isoclasses of indecomposable…
It contains the proof of a very general $\partial\bar\partial$-lemma, together with a decomposition theorem for currents with values in a (singular) Hermitian line bundle. As a corollary, we establish the K\"ahler version on an injectivity…
Zhang introduced semipositive metrics on a line bundle of a proper variety. In this paper, we generalize such metrics for a line bundle $L$ of a paracompact strictly $K$-analytic space $X$ over any non-archimedean field $K$. We prove…
We survey the use of continued fraction expansions in the algebraical and topological study of complex analytic singularities. We also prove new results, firstly concerning a geometric duality with respect to a lattice between plane…
Gardner, Gronchi and Zong posed the problem to find a discrete analogue of M. Meyer's inequality bounding the volume of a convex body from below by the geometric mean of the volumes of its slices with the coordinate hyperplanes. Motivated…
The notion of symmetry in polynomial rings with several indeterminates is generalized to polynomial rings over finite fields. Families of extensions of the projective line over a finite field of constants possessing this property are…
We prove a general result on irregularities of distribution for Borel sets intersected with bounded measurable sets or affine half-spaces.
The basic theory of semi-measures on locally compact Abelian groups is extended to prove the existence of a generalised Eberlein decomposition into such semi-measures.
We compare two known methods of extending a complex, unital, commutative normed algebra so as to include solutions to sets of monic polynomials over the original algebra. (One of these is a generalisation of a construction from the thesis…
I will give a new way to understand the Geometric Langlands Program.
We develop new characteristic-independent combinatorial criteria for semiampleness of divisors on $\overline{M}_{0,n}$. As an application, we associate to a cyclic rational quadratic form satisfying a certain balancedness condition an…