Séminaire Lotharingien de Combinatoire, 95B.99 (2026), 12 pp.
Dawei Shen, Mia Smith and David E. Speyer
Electroid Varieties and the Lagrangian Grassmannian
Abstract.
Recent work of Lam, Bychkov-Gorbounov-Kazakov-Talalaev, and
Chepuri-George-Speyer gave a stratification of the totally nonnegative
Lagrangian Grassmannian into electroid cells parameterized by cactus
networks, paralleling Postnikov's stratification of the totally nonnegative Grassmannian by positroid cells. Electroid varieties arise as an algebro-geometric extension of electroid cells. The combinatorics of these varieties was studied by Lam in 2018. We build on this work and study the geometric properties of electroid varieties. In analogy to results of Knutson, Lam, and Speyer on positroid varieties, we show that electroid varieties are reduced, irreducible, regular in codimension one, compatibly Frobenius split, and form a stratification.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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