Related papers: On absolute linear Harbourne constants

In this note we compute values of global linear Harbourne constants over arbitrary fields for up to ten lines. These invariants have appeared recently in the discussions around the Bounded Negativity Conjecture. They seem to be of…

In this note we exhibit the so-called Harbourne constants which capture and measure the Bounded Negativity on various birational models of an algebraic surface. We show an estimation for Harbourne constants for conic configurations on the…

In this note we find a bound for the so-called global linear Harbourne constants for smooth hypersurfaces in $\mathbb{P}^{3}_{\mathbb{C}}$

Let $X$ be a smooth projective surface and let $\mathcal{C}$ be an arrangement of curves on $X$. The Harbourne constant of $\mathcal{C}$ was defined as a way to investigate the occurrence of curves of negative self-intersection on blow ups…

The Bounded Negativity Conjecture predicts that for every complex projective surface $X$ there exists a number $b(X)$ such that $C^2\geq -b(X)$ holds for all reduced curves $C\subset X$. For birational surfaces $f:Y\to X$ there have been…

Similarly to the linear Harbourne constant recently defined, we study the elliptic $H$-constants of $\mathbb{P}^{2}$ and Abelian surfaces. We exhibit configurations of smooth plane cubic curves whose Harbourne index is arbitrarily close to…

The Bounded Negativity Conjecture predicts that for any smooth complex surface $X$ there exists a lower bound for the selfintersection of reduced divisors on $X$. This conjecture is open. It is also not known if the existence of such a…

We describe the effect of ramified morphisms on Harbourne constants of reduced effective divisors. With this goal, we introduce the pullback of a weighted cluster of infinitely near points under a dominant morphism between surfaces, and…

In this note we study the local negativity for certain configurations of smooth rational curves in smooth surfaces with numerically trivial canonical class. We show that for such rational curves there is a bound for the so-called local…

Boundary value problems for linear stationary dispersive equations of order $2l+1$, $l\in \mathbb{N}$ have been considered on finite intervals $(0,L)$. The existence and uniqueness of regular solutions have been established for general…

We construct and study curves with low H-constants on abelian and K3 surfaces. Using the Kummer $(16_{6})$-configurations on Jacobian surfaces and some $(16_{10})$-configurations of curves on $(1,3)$-polarized Abelian surfaces, we obtain…

We study the most general class of linear boundary-value problems for systems of $r$-th order ordinary differential equations whose solutions range over the complex H\"older space $C^{n+r,\alpha}$, with $0\leq n\in\mathbb{Z}$ and…

We prove explicit bounds on the number of lattice points on or near a convex curve in terms of geometric invariants such as length, curvature, and affine arclength. In several of our results we obtain the best possible constants. Our…

We show how positive unital linear maps can be used to obtain lower bounds for the maximum distance between the eigenvalues of two normal matrices. Some related bounds for the spread and condition number of Hermitian matrices are also…

The main goal of this paper is to present an algorithm bounding the dimension of a linear system of curves of given degree (or monomial basis) with multiple points in general position. As a result we prove the Hirschowitz--Harbourne…

In this work, we investigate the convergence of numerical approximations to coercivity constants of variational problems. These constants are essential components of rigorous error bounds for reduced-order modeling; extension of these…

Absolute value equations, due to their relation to the linear complementarity problem, have been intensively studied recently. In this paper, we present error bounds for absolute value equations. Along with the error bounds, we introduce an…

In this paper we study the concept of characteristic numbers and Chern slopes in the context of curve configurations in the real and complex projective plane. We show that some extremal line configurations inherit the same asymptotic…

Boundary value problems for the nonlinear Schrodinger equation on the half line in laboratory coordinates are considered. A class of boundary conditions that lead to linearizable problems is identified by introducing appropriate extensions…

This paper proposes hybrid high-order eigensolvers for the computation of guaranteed lower eigenvalue bounds. These bounds display higher order convergence rates and are accessible to adaptive mesh-refining algorithms. The involved…