An extension of the Siegel space of complex abelian varieties and conjectures on stability structures

© 2019, The Author(s). We study semi-algebraic domains associated with symplectic tori and conjecturally identified with spaces of stability conditions on the Fukaya categories of these tori. Our motivation is to test which results from the theory of flat surfaces could hold for more general spaces of stability conditions. The main results concern systolic bounds and volume of the moduli space.