Author

Marek Janasz

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Preprint Oct 2026

Geometry of some determinantal arrangements

Let $D_{m,n}\subset\C^{m\times n}$ be the union of the zero loci of the maximal minors of a generic $m\times n$ matrix, and let $U_{m,n}$ be its complement. We show that $U_{m,n}\cong\GL_m(\C)\times\Gr(m,n)^\circ$, where $\Gr(m,n)^\circ$ is the open stratum of the Grassmannian on which all Pl\"ucker coordinates are non...

Marek Janasz · 0 citations

Preprint Aug 2026

Simplicial arrangements in real projective three-space revisited

In this paper we study irreducible simplicial arrangements of projective planes in $\mathbb{P}^{3}(\mathbb{R})$ from combinatorial and projective geometry viewpoints. We first formulate a simpliciality criterion in terms of incidences between rank-two and rank-three flats, together with equivalent formulations using fa...

Marek Janasz, Piotr Pokora · 0 citations