20 citations · 89 across the 19 of their papers we have counts for
19 papers
Tropical KP Theory on Banana Curves
Simonetta Abenda, Türkü Özlüm Çelik, Claudia Fevola +1
The Kadomtsev-Petviashvili (KP) equation is the cornerstone of integrable systems, whose solutions reflect deep connections in algebraic geometry. Banana curves are reducible ratio…
Parametrization of positroid cells by Dubrovin-Natanzon Cartier divisors on maximal Mumford curves
Simonetta Abenda, Petr G. Grinevich
We prove that each totally positive Schubert cell is a real component of Jacobian of the maximal Mumford () curve corresponding to the Le-graph of such cell. At this a…
Geometric nature of relations on plabic graphs and totally non-negative Grassmannians
Simonetta Abenda, Petr G. Grinevich
The standard parametrization of totally non-negative Grassmannians was obtained by A. Postnikov [45] introducing the boundary measurement map in terms of discrete path integration…
Internal edge vectors on plabic networks in the disk and a generalization of Talaska formula
Simonetta Abenda, Petr G. Grinevich
Following [42], positroid cells ${\mathcal S}_{\mathcal M}^{\mbox{TNN}}$ in totally non-negative Grassmannians ${Gr^{\mbox{TNN}} (k,n)}$ admit parametrizations by positive weights…
Kasteleyn theorem, geometric signatures and KP-II divisors on planar bipartite networks in the disk
Simonetta Abenda
Maximal minors of Kasteleyn sign matrices on planar bipartite graphs in the disk count dimer configurations with prescribed boundary conditions, and the weighted version of such ma…
Real regular KP divisors on -curves and totally non-negative Grassmannians
Simonetta Abenda, Petr G. Grinevich
In this paper we construct an explicit map from planar bicolored (plabic) trivalent graphs representing a given irreducible positroid cell in the totally non-negative Grassmann…