Related papers: Kippenhahn's construction revisited

We give a new complexity bound for calculating the complex dimension of an algebraic set. Our algorithm is completely deterministic and approaches the best recent randomized complexity bounds. We also present some new, significantly sharper…

Let I be a conjugation-invariant ideal in the complex polynomial ring with variables z_1,...,z_n and their conjugates. The ideal I has the Quillen property if every real valued, strictly positive polynomial on the real zero set of I in C^n…

Membranes holomorphically embedded in flat noncompact space are constructed in terms of the degrees of freedom of an infinite collection of 0-branes. To each holomorphic curve we associate infinite-dimensional matrices which are static…

We obtain an upper bound for the volume of the convex hull of a simple closed Frenet curve with exactly four vertices, i.e., four points of vanishing torsion, and lying on the boundary of its convex hull. Moreover, we show that the upper…

On logarithmic paper some real algebraic curves look like smoothed broken lines. Moreover, the broken lines can be obtained as limits of those curves. The corresponding deformation can be viewed as a quantization, in which the broken line…

In 70's there was discovered a construction how to attach to some algebraic-geometric data an infinite-dimensional subspace in the space k((z)) of the Laurent power series. The construction was successfully used in the theory of integrable…

We consider the following problem in computational geometry: given, in the d-dimensional real space, a set of points marked as positive and a set of points marked as negative, such that the convex hull of the positive set does not intersect…

This note focuses on the problem of representing convex sets as projections of the cone of positive semidefinite matrices, in the particular case of sets generated by bivariate polynomials of degree four. Conditions are given for the convex…

In this note we investigate the convex hull of those $n \times n$-permutation matrices that correspond to symmetries of a regular $n$-gon. We give the complete facet description. As an application, we show that this yields a Gorenstein…

Efficient representations of convex sets are of crucial importance for many algorithms that work with them. It is well-known that sometimes, a complicated convex set can be expressed as the projection of a much simpler set in higher…

We analyze the correctness of an O(n log n) time divide-and-conquer algorithm for the convex hull problem when each input point is a location determined by a normal distribution. We show that the algorithm finds the convex hull of such…

We recall the theory of linear discrete Riemann surfaces and show how to use it in order to interpret a surface embedded in R^3 as a discrete Riemann surface and compute its basis of holomorphic forms on it. We present numerical examples,…

Convex geometries are closure systems satisfying the anti-exchange axiom. Every finite convex geometry can be embedded into a convex geometry of finitely many points in an n-dimensional space equipped with a convex hull operator, by the…

The characteristic numbers of smooth plane quartics are computed using intersection theory on a component of the moduli space of stable maps. This completes the verification of Zeuthen's prediction of characteristic numbers of smooth plane…

Using elementary duality properties of positive semidefinite moment matrices and polynomial sum-of-squares decompositions, we prove that the convex hull of rationally parameterized algebraic varieties is semidefinite representable (that is,…

A metrized complex of algebraic curves is a finite metric graph together with a collection of marked complete nonsingular algebraic curves, one for each vertex, the marked points being in bijection with incident edges. We establish a…

Given a smooth complex variety $X$, an algebraically skew embedding of $X$ is an embedding of $X$ into a complex projective space $\mathbb{P}^N$ such that for any two points $x,y\in X$, their embedded tangent spaces in $\mathbb{P}^N$ do not…

We prove an infinite-dimensional generalization of Zenger's lemma that was used in the proof of the fact that the convex hull of the point spectrum of a linear operator is contained in its numerical range. Two relevant examples are given,…

Convex polyhedra are the basis for several abstractions used in static analysis and computer-aided verification of complex and sometimes mission critical systems. For such applications, the identification of an appropriate…

In this article, we deal with the structure of the spherical Hall algebra of coherent sheaves with parabolic structures on a smooth projective curve of arbitrary genus. We provide a shuffle-like presentation of the vector bundle part and…