Claus Scheiderer

activity

19982023

most citedQuillen property of real algebraic varieties

8 citations · 39 across the 23 of their papers we have counts for

collaborators

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18 papers · 1 filter

math.AG2019

Two remarks on sums of squares with rational coefficients

Jose Capco, Claus Scheiderer

There exist homogeneous polynomials $f$ with $Q$ -coefficients that are sums of squares over $R$ but not over $Q$ . The only systematic construction of such p…

math.AG2018★ 1 cited

Real tropicalization and analytification of semialgebraic sets

Philipp Jell, Claus Scheiderer, Josephine Yu

Let $K$ be a real closed field with a nontrivial non-archimedean absolute value. We study a refined version of the tropicalization map, which we call real tropicalization map, that…

math.AG2017

A Positivstellensatz for forms on the positive orthant

Claus Scheiderer, Colin Tan

Let $p$ be a nonconstant form in $R [x_{1}, \dots, x_{n}]$ with $p (1, \dots, 1) > 0$ . If $p^{m}$ has strictly positive coefficients for some integer $m \geq 1$ , we show that $p^{m}$ has str…

math.AG2016

Polynomials nonnegative on the cylinder

Claus Scheiderer, Sebastian Wenzel

In 2010, Marshall settled the strip conjecture, according to which every polynomial in $R [x, y]$ , nonnegative on the strip $[- 1, 1] \times R$ , is a sum of squares and…

math.AG2016

Sum of squares length of real forms

Claus Scheiderer

For $n, d \geq 1$ let $p (n, 2 d)$ denote the smallest number $p$ such that every sum of squares of forms of degree $d$ in $R [x_{1}, \dots, x_{n}]$ is a sum of $p$ squares. We establ…

math.AG2016★ 1 cited

An observation on positive definite forms

Claus Scheiderer

Given two positive definite forms $f, g \in R [x_{1}, \dots, x_{n}]$ , we prove that $f g^{r}$ lies in the interior of the sums of squares cone for large $r$ .