Author

A. Giannoni

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Preprint Oct 2026

Maximum 2-scattered subspaces of $V(r,q^6)$ for every $r\geq 3$

We prove that for every prime power $q$ and every integer $r\geq 3$ there exists a maximum $2$-scattered $\mathbb{F}_q$-subspace of $V(r,q^6)$, that is, a $2r$-dimensional $\mathbb{F}_q$-subspace meeting every $2$-dimensional $\mathbb{F}_{q^6}$-subspace in dimension at most $2$. Since an example in dimension three is k...

Daniele Bartoli, Francesco Ghiandoni, A. Giannoni et al. · 0 citations

Preprint Oct 2026

The weak cylinder conjecture for polynomial graphs of bounded degree

Ball's weak cylinder conjecture asserts that a set of $p^2$ points in $\mathrm{AG}(3,p)$ with at least $p$ non-determined directions is a union of $p$ parallel lines. We prove the conjecture for sets admitting a polynomial graph representation of total degree at most $D$, provided that $p>D^{9/2}$. More precisely, a no...

Daniele Bartoli, A. Giannoni · 0 citations

Preprint Sep 2026

F-sets of arbitrary finite width

Ferraguti and Micheli conjectured that non-trivial $F$-sets of every prescribed width exist over each finite field. We prove the finite-width part of their conjecture over $\mathbb{F}_q$ for every $q\neq2,3$. Fix a suitable prime $\ell$. For a degree bound $D$, we consider the saturated family of all irreducible polyno...

A. Giannoni · 0 citations