25 citations · 181 across the 41 of their papers we have counts for
10 papers · 1 filter
Rational tensegrities through the lens of toric geometry
Fatemeh Mohammadi, Xian Wu
A classical tensegrity model consists of an embedded graph in a vector space with rigid bars representing edges, and an assignment of a stress to every edge such that at every vert…
K-polynomials of multiplicity-free varieties
Federico Castillo, Yairon Cid-Ruiz, Fatemeh Mohammadi +1
We describe the twisted -polynomial of multiplicity-free varieties in a multiprojective setting. More precisely, for multiplicity-free varieties, we show that the support of the…
Toric degenerations of partial flag varieties and combinatorial mutations of matching field polytopes
Oliver Clarke, Fatemeh Mohammadi, Francesca Zaffalon
We study toric degenerations arising from Gröbner degenerations or the tropicalization of partial flag varieties. We produce a new family of toric degenerations of partial flag var…
A study of nonlinear multiview varieties
Yairon Cid-Ruiz, Oliver Clarke, Fatemeh Mohammadi
We study the nonlinear generalization of the classical multiview variety, which is a fundamental concept in computer vision. In this paper, we take the first comprehensive step to…
Toric and tropical Bertini theorems in positive characteristic
Francesca Gandini, Milena Hering, Diane Maclagan +4
We generalize the toric Bertini theorem of Fuchs, Mantova, and Zannier to positive characteristic. A key part of the proof is a new algebraically closed field containing the field…
Standard monomial theory and toric degenerations of Richardson varieties in flag varieties
Narasimha Chary Bonala, Oliver Clarke, Fatemeh Mohammadi
We study standard monomial bases for Richardson varieties inside the flag variety. In general, writing down a standard monomial basis for a Richardson variety can be challenging, a…
Standard monomial theory and toric degenerations of Richardson varieties inside Grassmannians and flag varieties
Narasimha Chary Bonala, Oliver Clarke, Fatemeh Mohammadi
We study toric degenerations of opposite Schubert and Richardson varieties inside degenerations of Grassmannians and flag varieties. These degenerations are parametrized by matchin…
Families of Gröbner Degenerations, Grassmannians and Universal Cluster Algebras
Lara Bossinger, Fatemeh Mohammadi, Alfredo Nájera Chávez
Let be the weighted projective variety defined by a weighted homogeneous ideal and a maximal cone in the Gröbner fan of with rays. We construct a flat family ov…
Toric degenerations of Grassmannians from matching fields
Fatemeh Mohammadi, Kristin Shaw
We study the algebraic combinatorics of monomial degenerations of Plücker forms which is governed by matching fields in the sense of Sturmfels and Zelevinsky. We provide a necessar…
Computing toric degenerations of flag varieties
Lara Bossinger, Sara Lamboglia, Kalina Mincheva +1
We compute toric degenerations arising from the tropicalization of the full flag varieties and embedded in a product of Grassmannians. For $…