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

TL;DR

This paper explores semi-algebraic domains linked to symplectic tori, aiming to understand stability conditions and their geometric properties, with a focus on systolic bounds and moduli space volume.

Contribution

It extends the Siegel space framework to symplectic tori and investigates conjectural links with stability condition spaces, testing geometric results in this broader context.

Findings

Establishment of systolic bounds for the studied domains

Analysis of volume properties of the associated moduli space

Conjectural identification of these domains with stability condition spaces

Abstract

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.