Compactifications of $M_{0,n}$ associated with Alexander self-dual complexes: Chow ring, $\psi$-classes and intersection numbers

TL;DR

This paper introduces ASD compactifications of the moduli space M_{0,n} derived from Alexander self-dual complexes, providing explicit Chow ring descriptions, studying tautological bundles, and deriving intersection number recursions.

Contribution

It offers the first explicit description of Chow rings for ASD compactifications and develops new tools for intersection theory on these spaces.

Findings

Explicit Chow ring formulas for ASD compactifications

Computed Chern classes and top intersections of tautological bundles

Derived recursion relations for intersection numbers

Abstract

An Alexander self-dual complex gives rise to a compactification of $M_{0,n}$, called ASD compactification, which is a smooth algebraic variety. ASD compactifications include (but are not exhausted by) the polygon spaces, or the moduli spaces of flexible polygons. We present an explicit description of the Chow rings of ASD compactifications. We study the analogues of Kontsevich tautological bundles, compute their Chern classes, compute top intersections of the Chern classes, and derive a recursion for the intersection numbers.