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math.AG2026
A construction of polyptych lattices via a pair of Gorenstein PL cones
Laura Escobar, Megumi Harada, Christopher Manon
The theory of polyptych lattices seeks to incorporate, into a single combinatorial framework, the piecewise-linear bijections (mutations) that appear in many theories that generali…
math.AG2024
Gorenstein-Fano polytopes and compactifications of rank 2 polyptych lattices
Adrian Cook, Laura Escobar, Megumi Harada +1
The theory of polyptych lattices was introduced by Escobar, Harada, and Manon, in an effort to simultaneously generalize combinatorial and geometric phenomena seen in toric, cluste…
math.AG2024
Geometric families of degenerations from mutations of polytopes
Laura Escobar, Megumi Harada, Christopher Manon
We introduce the notion of a polyptych lattice, which encodes a collection of lattices related by piecewise linear bijections. We also define and study PL (polyptych-lattice) polyt…