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math.CO2025
Varieties of Lines in 3-Space
Benjamin Hollering, Elia Mazzucchelli, Matteo Parisi +1
We consider configurations of lines in 3-space with incidences prescribed by a graph. This defines a subvariety in a product of Grassmannians. Leveraging a connection with rigidity…
math.CO2025
Exterior Cyclic Polytopes and Convexity of Amplituhedra
Elia Mazzucchelli, Elizabeth Pratt
The amplituhedron is a semialgebraic set in the Grassmannian. We study convexity and duality of amplituhedra. We introduce a notion of convexity, called \textit{extendable convexit…