相关论文: Effective Bounds of Linear Series on Algebraic Var…

Upper bounds on the maximum number of codewords in a binary code of a given length and minimum Hamming distance are considered. New bounds are derived by a combination of linear programming and counting arguments. Some of these bounds…

We obtain restriction results of K. de Leeuw's type for maximal operators defined through multilinear Fourier multipliers of either strong or weak type acting on weighted Lebesgue spaces. We give some application of our development. In…

In this paper, we explore several threads arising from our recent joint work on arithmetic holonomy bounds, which were originally devised to prove new irrationality results based on the method of Ap\'ery limits. We propose a new method to…

In this paper we extend the arithmetic intersection theory of adelic divisors on quasiprojective varieties developed by X. Yuan and S. W. Zhang to cover certain adelic arithmetic divisors that are not nef nor integrable. The key concept…

We compute the (unbounded) Newton-Okounkov body of the Hilbert scheme of points on $\mathbb C^2$. We obtain an upper bound for the Newton-Okounkov body of the Hilbert scheme of points on any smooth toric surface. We conjecture that this…

Building on results of Arthur and Mok, we extend to (finite volume) complex and quaternionic hyperbolic manifolds the results of arXiv:1004.1085. For the spherical spectrum our results are optimal. Finally, as an application we prove a…

We establish a finiteness result for pointed maps to the base space $U$ of a smooth projective family of varieties with maximal variation in moduli. For its proof, we establish the rigidity of pointed maps to a (not necessarily compact)…

We develop a number of inequalities to obtain bounds for the numerical radius of a bounded linear operator defined on a complex Hilbert space using the properties of $t$-Aluthge transform. We show that the bounds obtained are sharper than…

In this article we investigate Hirzebruch-Riemann-Roch formulae for line bundles on irreducible symplectic K\"ahler manifolds. As Huybrechts has shown, for every irreducible complex K\"ahler manifold $X$ of dimension $2n$, there are numbers…

Minimal linear codes are in one-to-one correspondence with special types of blocking sets of projective spaces over a finite field, which are called strong or cutting blocking sets. In this paper we prove an upper bound on the minimal…

It is a well established fact, that any projective algebraic variety is a moduli space of representations over some finite dimensional algebra. This algebra can be chosen in several ways. The counterpart in algebraic geometry is…

In this paper, we develop several pluripotential-theoretic techniques for singular metrics on vector bundles. We first introduce the theory of non-pluripolar products on holomorphic vector bundles on complex manifolds. Then we define and…

This paper investigates realisations of elliptic differential operators of general order on manifolds with boundary following the approach of B\"ar-Ballmann to first order elliptic operators. The space of possible boundary values of…

In this short note, we show that, assuming a conjecture of Arcara and Miles, a line bundle on a smooth complex projective surface admits a deformed Hermitian-Yang-Mills metric if and only if it is stable in the ``large scaling limit" with…

Let L be an ample holomorphic line bundle over a compact complex Hermitian manifold X. Any fixed smooth Hermitian metric on L induces a Hilbert space structure on the space of global holomorphic sections with values in the k:th tensor power…

We study extension properties for morphisms of stacks of bundles for group algebraic spaces. Applications are a short proof of the classification of bundles on the projective line for smooth geometrically reductive groups and the existence…

We use techniques from algebraic and extremal combinatorics to derive upper bounds on the number of independent sets in several (hyper)graphs arising from finite geometry. In this way, we obtain asymptotically sharp upper bounds for partial…

In an earlier work, the first author and Petsche used potential theoretic techniques to establish a lower bound for the height of algebraic numbers that satisfy splitting conditions, such as being totally real or p-adic, improving on…

Let $Z$ be an algebraic subvariety of a Shimura variety. We extend results of the first author to prove an effective upper bound for the degree of a non-facteur maximal special subvariety of $Z$.

We shall give an explicit estimate of the lower bound of the Bergman kernel associated to a positive line bundle. In the compact Riemann surface case, our result can be seen as an explicit version of Tian's partial $C^0$-estimate.