Zobrazeno 1 - 10
of 79
pro vyhledávání: '"PLAUMANN, DANIEL"'
Every polygon with n vertices in the complex projective plane is naturally associated with its adjoint curve of degree n-3. Hence the adjoint of a heptagon is a plane quartic. We prove that a general plane quartic is the adjoint of exactly 864 distin
Externí odkaz:
http://arxiv.org/abs/2408.15759
Given a real algebraic curve, embedded in projective space, we study the computational problem of deciding whether there exists a hyperplane meeting the curve in real points only. More generally, given any divisor on such a curve, we may ask whether
Externí odkaz:
http://arxiv.org/abs/2106.13990
We study families of faces for convex semi-algebraic sets via the normal cycle which is a semi-algebraic set similar to the conormal variety in projective duality theory. We propose a convex algebraic notion of a "patch" -- a term recently coined by
Externí odkaz:
http://arxiv.org/abs/2104.13306
Publikováno v:
SIAM Journal on Applied Algebra and Geometry 5:1 (2021), 86-113
Kippenhahn's Theorem asserts that the numerical range of a matrix is the convex hull of a certain algebraic curve. Here, we show that the joint numerical range of finitely many Hermitian matrices is similarly the convex hull of a semi-algebraic set.
Externí odkaz:
http://arxiv.org/abs/1907.04768
Autor:
Dey, Papri, Plaumann, Daniel
Hyperbolic polynomials are real multivariate polynomials with only real roots along a fixed pencil of lines. Testing whether a given polynomial is hyperbolic is a difficult task in general. We examine different ways of translating hyperbolicity into
Externí odkaz:
http://arxiv.org/abs/1810.04055
Publikováno v:
Pacific J. Math. 303 (2019) 243-263
We describe a new method for constructing a spectrahedral representation of the hyperbolicity region of a hyperbolic curve in the real projective plane. As a consequence, we show that if the curve is smooth and defined over the rational numbers, then
Externí odkaz:
http://arxiv.org/abs/1807.10901
We present a computational study of smooth curves of degree six in the real projective plane. In the Rokhlin-Nikulin classification, there are 56 topological types, refined into 64 rigid isotopy classes. We developed software that determines the topo
Externí odkaz:
http://arxiv.org/abs/1703.01660
Autor:
Naldi, Simone, Plaumann, Daniel
Publikováno v:
Journal of Algebra and its Applications, 2017
Hyperbolic programming is the problem of computing the infimum of a linear function when restricted to the hyperbolicity cone of a hyperbolic polynomial, a generalization of semidefinite programming. We propose an approach based on symbolic computati
Externí odkaz:
http://arxiv.org/abs/1612.07340
Publikováno v:
Contemporary Mathematics Vol. 697, p.81-105 (2017)
Representations of nonnegative polynomials as sums of squares are central to real algebraic geometry and the subject of active research. The sum-of-squares representations of a given polynomial are parametrized by the convex body of positive semidefi
Externí odkaz:
http://arxiv.org/abs/1608.00234
A celebrated result by Hilbert says that every real nonnegative ternary quartic is a sum of three squares. We show more generally that every nonnegative quadratic form on a real projective variety $X$ of minimal degree is a sum of $\dim(X)+1$ squares
Externí odkaz:
http://arxiv.org/abs/1606.04387