Zobrazeno 1 - 10
of 21
pro vyhledávání: '"Vill, Julian"'
Autor:
Kahle, Thomas, Vill, Julian
We propose an effective algorithm that decides if a prime ideal in a polynomial ring over the complex numbers can be transformed into a toric ideal by a linear automorphism of the ambient space. If this is the case, the algorithm computes such a tran
Externí odkaz:
http://arxiv.org/abs/2408.14323
Autor:
Kowalczyk, Tomasz, Vill, Julian
We show that the higher Pythagoras numbers for the polynomial ring are infinite $p_{2s}(K[x_1,x_2,\dots,x_n])=\infty$ provided that $K$ is a formally real field, $n\geq2$ and $s\geq 1$. This almost fully solves an old question \cite[Problem 8]{cldr19
Externí odkaz:
http://arxiv.org/abs/2311.07356
Autor:
Vill, Julian
Given a subspace $U\subset\mathbb{C}[x_1,\dots,x_n]_d$ we consider the closure of the image of the rational map $\mathbb{P}^{n-1}\dashrightarrow\mathbb{P}^{\dim U-1}$ given by $U$. Its coordinate ring is isomorphic to $\bigoplus_{i\ge 0} U^i$ where $
Externí odkaz:
http://arxiv.org/abs/2304.02332
Autor:
Vill, Julian
Given a linear map on the vector space of symmetric matrices, every fiber intersected with the set of positive semidefinite matrices is a spectrahedron. Using the notion of the fiber body we can build the average over all such fibers and thereby cons
Externí odkaz:
http://arxiv.org/abs/2303.05815
We introduce a family of discrete context-specific models, which we call decomposable. We construct this family from the subclass of staged tree models known as CStree models. We give an algebraic and combinatorial characterization of all context-spe
Externí odkaz:
http://arxiv.org/abs/2210.11521
Autor:
Vill, Julian
Publikováno v:
Journal of Symbolic Computation, Volume 116, 263-283, 2023
The Gram spectrahedron of a real form $f\in\mathbb{R}[\underline{x}]_{2d}$ parametrizes all sum of squares representations of $f$. It is a compact, convex, semi-algebraic set, and we study its facial structure in the case of ternary quartics, i.e. $f
Externí odkaz:
http://arxiv.org/abs/2112.10533
The variety $ \mathrm{Sing}_{n, m} $ consists of all tuples $ X = (X_1,\ldots, X_m) $ of $ n\times n $ matrices such that every linear combination of $ X_1,\ldots, X_m $ is singular. Equivalently, $X\in\mathrm{Sing}_{n,m}$ if and only if $\det(\lambd
Externí odkaz:
http://arxiv.org/abs/2106.00735
Autor:
Vill, Julian
Let $f\in\Sigma_{n,2d}$ be a sum of squares. The Gram spectrahedron of $f$ is a compact, convex set that parametrizes all sum of squares representations of $f$. Let $F\subseteq\mathrm{Gram}(f)$ be a face of its Gram spectrahedron. We are interested i
Externí odkaz:
http://arxiv.org/abs/2008.10315
Publikováno v:
In Linear Algebra and Its Applications 1 September 2022 648:56-69
