2021/01/18 by Roberta Di Gennaro, Giovanna Ilardi, Di Gennaro, Roberta +8
Mathematics · #13A15 #13C70 #14C20 #14E05 #14J70 #14N20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Tensor decomposition and applications #math.AG #msc:13A15 #msc:13C70 #msc:14C20 #msc:14E05 #msc:14J70 #msc:14N20
paper · pdf · doi:10.48550/arxiv.2101.07346
Revised version following advices by the referees. Accepted for publication in JPAA
openalex publication_date 2021/01/18 · arxiv created 2022/02/08 · arxiv updated 2022/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Unexpected hypersurfaces are a brand name for some special linear systems. They were introduced around 2017 and are a field of intensive study since then. They attracted a lot of attention because of their close tights to various other areas of mathematics including vector bundles, arrangements of hyperplanes, geometry of projective varieties. Our research is motivated by the what is now known as the BMSS duality, which is a new way of deriving projective varieties out of already constructed. The last author coined the concept of companion surfaces in the setting of unexpected curves admitted by the B3 root system. Here we extend this construction in various directions. We revisit the configurations of points associated to either root systems or to Fermat arrangements and we study the geometry of the associated varieties and their companions.