Fabio Vlacci

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math.CV2025

A Strong Version of the Hilbert Nullstellensatz for slice regular polynomials in several quaternionic variables

Anna Gori, Giulia Sarfatti, Fabio Vlacci

In this paper we prove a strong version of the Hilbert Nullstellensatz in the ring $H [q_{1}, \dots, q_{n}]$ of slice regular polynomials in several quaternionic variables. Our p…

math.CV2025

Quaternionic Cartan coverings and applications

Jasna Prezelj, Fabio Vlacci

We present the topological foundations for the solvability of Multiplicative Cousin problems formulated on an axially symmetric domain $I^c ◯ \subset H .$ In particular, we prov…

math.CV2024

Vanishing of quaternionic cohomology groups and applications

Jasna Prezelj, Fabio Vlacci

We present solutions to additive and multiplicative Cousin problems formulated on an axially symmetric domain $I^c ◯ \subset H$ for slice--regular functions starting from the s…