3 citations · 8 across the 9 of their papers we have counts for
10 papers
The Self-Projecting Grassmannian
Alheydis Geiger, Francesca Zaffalon
We introduce the self-projecting Grassmannian, an irreducible subvariety of the Grassmannian parametrizing linear subspaces that satisfy a generalized self-duality condition. We st…
Real Tropical Quartics and their Bitangents: Counting with Patchworking
Alheydis Geiger
For certain tropical quartic curves the existing techniques could not predict the lifting behavior of their bitangents over the real numbers. We close this gap by using patchworkin…
Graph Curve Matroids
Alheydis Geiger, Kevin Kuehn, Raluca Vlad
We introduce a new class of matroids, called graph curve matroids. A graph curve matroid is associated to a graph and defined on the vertices of the graph as a ground set. We prove…
Positive del Pezzo Geometry
Nick Early, Alheydis Geiger, Marta Panizzut +2
Real, complex, and tropical algebraic geometry join forces in a new branch of mathematical physics called positive geometry. We develop the positive geometry of del Pezzo surfaces…
Self-dual matroids from canonical curves
Alheydis Geiger, Sachi Hashimoto, Bernd Sturmfels +1
Self-dual configurations of 2n points in a projective space of dimension n-1 were studied by Coble, Dolgachev-Ortland, and Eisenbud-Popescu. We examine the self-dual matroids and s…
Computing tropical bitangents to smooth quartic curves in polymake
Alheydis Geiger, Marta Panizzut
In this article we introduce the recently developed polymake extension TropicalQuarticCurves and its associated database entry in polyDB dealing with smooth tropical quartic curves…
A tropical count of real bitangents to plane quartic curves
Alheydis Geiger, Marta Panizzut
A smooth tropical quartic curve has seven tropical bitangent classes. Their shapes can vary within the same combinatorial type of curve. We study deformations of these shapes and w…
Towards tropically counting binodal surfaces
Madeline Brandt, Alheydis Geiger
Tropical counting tools are useful for many enumerative questions. We count tropical multinodal surfaces using floor plans, looking at the case when two nodes are tropically close…
A Tropical Count of Binodal Cubic Surfaces
Madeline Brandt, Alheydis Geiger
There are 280 binodal cubic surfaces passing through 17 general points. For the typically used tropical point conditions, we show that 214 of these give tropicalizations such that…
On realizability of lines on tropical cubic surfaces and the Brundu-Logar normal form
Alheydis Geiger
We present results on the relative realizability of infinite families of lines on general smooth tropical cubic surfaces. Inspired by the problem of relative realizability of lines…