Author

R. van Dobben de Bruyn

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Preprint Aug 2026

Divisors in projective bundles over the projective line whose complement is affine space

Given a smooth projective variety $X$ of dimension $n$ and a closed subscheme $Z \subseteq X$, it is in general a difficult problem to determine whether $X \setminus Z$ is isomorphic to $\mathbf A^n$. In the case where $X$ is a projective bundle over $\mathbf P^1$ and the restriction of every irreducible component of $...

R. van Dobben de Bruyn · 2 citations

Preprint Sep 2026

Mermin-Peres magic rectangles modulo odd primes

The Mermin-Peres magic square provides a simple example of a system of linear equations over $\mathbb{Z}/2\mathbb{Z}$ which has no classical solutions but does have a finite-dimensional operator solution. For a long time, it was not known how to construct similar examples over $\mathbb{Z}/d\mathbb{Z}$ with $d$ odd. In...

Josse van Dobben de Bruyn, R. van Dobben de Bruyn, Peter Zeman · 2 citations