AStab(C) is a partial compactification of Stab(C)/C built from multiscale decompositions, and the manifold-with-corners conjecture describing its boundary is proved at generic admissible points.
[BCG+] Matt Bainbridge, Dawei Chen, Quentin Gendron, Samuel Grushevsky, and Martin Möller,The moduli space of multi-scale differentials,
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The Space of augmented stability conditions
AStab(C) is a partial compactification of Stab(C)/C built from multiscale decompositions, and the manifold-with-corners conjecture describing its boundary is proved at generic admissible points.