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Computing toric degenerations of flag varieties

- Lara Bossinger, Sara Lamboglia, Kalina Mincheva, F. Mohammadi
- Mathematics
- 17 February 2017

We compute toric degenerations arising from the tropicalization of the full flag varieties \(\mathop{\mathrm{Fl}}\nolimits _{4}\) and \(\mathop{\mathrm{Fl}}\nolimits _{5}\) embedded in a product of… Expand

Toric Degenerations of Gr(2, n) and Gr(3, 6) via Plabic Graphs

- Lara Bossinger, X. Fang, G. Fourier, Milena Hering, M. Lanini
- Mathematics
- 12 December 2016

We establish an explicit bijection between the toric degenerations of the Grassmannian Gr(2, n) arising from maximal cones in tropical Grassmannians and the ones coming from plabic graphs… Expand

String cone and superpotential combinatorics for flag and Schubert varieties in type A

- Lara Bossinger, G. Fourier
- Computer Science, Mathematics
- J. Comb. Theory, Ser. A
- 20 November 2016

TLDR

The degree of the Hilbert-Poincar\'e polynomial of PBW-graded modules

- T. Backhaus, Lara Bossinger, C. Desczyk, G. Fourier
- Mathematics
- 5 August 2014

In this note, we study the Hilbert-Poincar\'e polynomials for the PBW-graded of simple modules for a simple complex Lie algebra. The computation of their degree can be reduced to modules of… Expand

Toric degenerations of cluster varieties and cluster duality

- Lara Bossinger, Bosco Fr'ias-Medina, Timothy Magee, Alfredo Nájera Chávez
- Mathematics
- Compositio Mathematica
- 22 September 2018

We introduce the notion of a $Y$-pattern with coefficients and its geometric counterpart: an $\mathcal {X}$-cluster variety with coefficients. We use these constructions to build a flat degeneration… Expand

Families of Gröbner Degenerations, Grassmannians and Universal Cluster Algebras

- Lara Bossinger, F. Mohammadi, Alfredo N'ajera Ch'avez
- Mathematics
- 29 July 2020

Let $V$ be the weighted projective variety defined by a weighted homogeneous ideal $J$ and $C$ a maximal cone in the Grobner fan of $J$ with $m$ rays. We construct a flat family over $\mathbb A^m$… Expand

Birational sequences and the tropical Grassmannian

- Lara Bossinger
- Mathematics
- 28 March 2019

We introduce iterated sequences for Grassmannians, a new class of Fang-Fourier-Littelmanns' birational sequences and explain how they give rise to points in $\text{trop}(\text{Gr}(k,\mathbb C^n))$,… Expand

Full-Rank Valuations and Toric Initial Ideals

- Lara Bossinger
- Mathematics
- 26 March 2019

Let $V(I)$ be a polarized projective variety or a subvariety of a product of projective spaces and let $A$ be its (multi-)homogeneous coordinate ring. Given a full-rank valuation $\mathfrak v$ on $A$… Expand

R T ] 2 8 M ar 2 01 9 Birational sequences and the tropical Grassmannian

- Lara Bossinger
- 2019

We introduce iterated sequences for Grassmannians, a new class of Fang-Fourier-Littelmanns’ birational sequences and explain how they give rise to points in trop(Gr(k,C)), Speyer-Sturmfels’ tropical… Expand

Mini-Workshop: Superpotentials in Algebra and Geometry

- Lara Bossinger, Eduardo Gonzalez, K. Rietsch, L. Williams
- Mathematics
- 9 February 2021

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