Julian Vill

collaborators

3 papers

math.AG2023

On higher Pythagoras numbers of polynomial rings

Tomasz Kowalczyk, Julian Vill

We show that the higher Pythagoras numbers for the polynomial ring are infinite $p_{2 s} (K [x_{1}, x_{2}, \dots, x_{n}]) = \infty$ provided that $K$ is a formally real field, $n \geq 2$ and $s\ge…

math.AC2023

Bounds on Hilbert functions with application to convexity

Julian Vill

Given a subspace $U \subset C [x_{1}, \dots, x_{n}]_{d}$ we consider the closure of the image of the rational map $P^{n - 1} ⇢ P^{d i m U - 1}$ given by $U$ .…

math.AC2021

Ideals of Spaces of Degenerate Matrices

Julian Vill, Mateusz Michałek, Alexander Taveira Blomenhofer

The variety $Sing_{n, m}$ consists of all tuples $X = (X_{1}, \dots, X_{m})$ of $n \times n$ matrices such that every linear combination of $X_{1}, \dots, X_{m}$ is singula…