Year: 2026
Type: preprint
Abstract: Associated to small extended Dynkin quivers, we construct series of Fano varieties of fixed Picard rank at most five and arbitrary even dimension, which admit a very explicit description of their geometry. For example, they all admit a flat morphism to a projective space, whose general fiber is a product of projective lines. We also give a closed formula for all Betti numbers, and interpret this formula in terms of an action of a cohomological Hall algebra on the cohomology of all the varieties in a series.
Source: arXiv (Cornell University)
Authors: Belmans, Pieter, Reineke, Markus
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222464687