Tomasz Kowalczyk

collaborators

3 papers

math.AG2026

A note on the real Jacobian conjecture in degree 7

Tomasz Kowalczyk

Let $(p, q)$ be a Jacobian pair. We show that the real Jacobian conjecture holds if the degree of $p$ is 7 and the highest degree homogenous part is of the form $α x^{7} + β x^{6} y$ for $…

math.AC2026

Sums of squares on curves and surfaces

BartÅomiej Bychawski, Bartosz GÅowacki, Tomasz Kowalczyk

We study sums of higher even powers in the coordinate rings of singular planar curves $x^{M} = y^{m}$ for coprime positive integers $m < M$ . We then show that the $2 s$ -Pythagoras number of…

math.AG2025

Sums of squares of regular functions on rational surfaces

Tomasz Kowalczyk

We study the sums of squares on cylinders of the form $X \times A_{K}$ for a (weakly) factorial curve $C$ . We prove the equality of the Pythagoras numbers of the ring of reg…