15 citations · 47 across the 12 of their papers we have counts for
13 papers
Torus actions on compactified braid varieties and polytopality of subword complexes
Lara Bossinger, Mikhail Gorsky, José Simental
Every cluster variety admits an action of its cluster dilation group. We prove that, in the case of braid varieties for simple Lie groups, this action always extends to a regular a…
Tropical initial degeneration for systems of algebraic differential equations
Lara Bossinger, Sebastian Falkensteiner, Cristhian Garay-López +1
We study the notion of degeneration for affine schemes associated to systems of algebraic differential equations with coefficients in the fraction field of a multivariate formal po…
Newton--Okounkov bodies and minimal models for cluster varieties
Lara Bossinger, Man-Wai Cheung, Timothy Magee +1
Let be a (partial) minimal model of a scheme with a cluster structure. Under natural assumptions, for every choice of seed we associate a Newton--Okounkov body to every div…
Infinite matroids in tropical differential algebra
F. Aroca, L. Bossinger, S. Falkensteiner +3
We consider a finite-dimensional vector space over an arbitrary field and an arbitrary set . We show that the set consisting of the minimal…
A survey on toric degenerations of projective varieties
Lara Bossinger
In this survey I summarize the constructions of toric degenerations obtained from valuations and Gröbner theory and describe in which sense they are equivalent. I show how adapted…
Maps to toric varieties, toric degenerations and integrable systems à la Harada--Kaveh
Takuya Murata, Lara Bossinger
Given a toric degeneration (a degeneration to a toric variety), over the complex numbers, we construct a surjective continuous map from a general fiber to the special fiber of the…
Tropical totally positive cluster varieties
Lara Bossinger
We study the relation between the integer tropical points of a cluster variety (satisfying the full Fock-Goncharov conjecture) and the totally positive part of the tropicalization…
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…
Birational sequences and the tropical Grassmannian
Lara Bossinger
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}(…
Full-rank Valuations and Toric Initial Ideals
Lara Bossinger
Let be a polarized projective variety or a subvariety of a product of projective spaces and let be its (multi-)homogeneous coordinate ring. Given a full-rank valuation $…
Toric degenerations of cluster varieties and cluster duality
Lara Bossinger, Bosco Frías-Medina, Timothy Magee +1
We introduce the notion of a -pattern with coefficients and its geometric counterpart: a cluster -variety with coefficients. We use these constructions to build a f…
Toric degenerations: a bridge between representation theory, tropical geometry and cluster algebras
Lara Bossinger
In this thesis we study toric degenerations of projective varieties. We compare different constructions to understand how and why they are related as s first step towards developin…
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 $…