Series of Fano quiver moduli from extended Dynkin quivers

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.