12 citations · 23 across the 15 of their papers we have counts for
17 papers
Tropical Abel-Jacobi theory
Omid Amini, Daniel Corey, Leonid Monin
To a compact tropical variety of arbitrary dimension, we associate a collection of intermediate Jacobians defined in terms of tropical homology and tropical monodromy. We then deve…
Regular subdivisions, bounds on initial ideals, and categorical limits
George Balla, Daniel Corey, Igor Makhlin +1
Several known constructions relate initial degenerations of projective toric varieties and Grassmannians to regular subdivisions of appropriate point configurations. We define a ge…
Matroids in OSCAR
Daniel Corey, Lukas Kühne, Benjamin Schröter
OSCAR is an innovative new computer algebra system which combines and extends the power of its four cornerstone systems - GAP (group theory), Singular (algebra and algebraic geomet…
Singular matroid realization spaces
Daniel Corey, Dante Luber
We study smoothness of realization spaces of matroids for small rank and ground set. For -realizable matroids, when the rank is , we prove that the realization space…
The virtual Euler characteristic for binary matroids
Madeline Brandt, Juliette Bruce, Daniel Corey
Inspired by Kontsevich's graphic orbifold Euler characteristic we define a virtual Euler characteristic for any finite set of isomorphism classes of matroids of rank . Our main…
Counting tropical curves in : computation & polynomiality properties
Daniel Corey, Hannah Markwig, Dhruv Ranganathan
Counts of curves in with fixed contact order with the toric boundary and satisfying point conditions can be determined with tropical methods by Mik…
Initial degenerations of flag varieties
Daniel Corey, Jorge Alberto Olarte
We prove that the initial degenerations of the flag variety admit closed immersions into finite inverse limits of flag matroid strata, where the diagrams are derived from matroidal…
The Grassmannian of 3-planes in is schön
Daniel Corey, Dante Luber
We prove that the open subvariety of the Grassmannian determined by the nonvanishing of all Plücker coordinates is schön, i.e.,…
The Ceresa class and tropical curves of hyperelliptic type
Daniel Corey, Wanlin Li
We define a new algebraic invariant of a graph called the Ceresa-Zharkov class and show that it is trivial if and only if is of hyperelliptic type, equivalently, does n…
Syzygies of : data and conjectures
Juliette Bruce, Daniel Corey, Daniel Erman +3
We provide a number of new conjectures and questions concerning the syzygies of . The conjectures are based on computing the graded Betti tables an…
Initial degenerations of spinor varieties
Daniel Corey
We construct closed immersions from initial degenerations of the spinor variety to inverse limits of strata associated to even -matroids. As an application, we pr…
The Ceresa class: tropical, topological, and algebraic
Daniel Corey, Jordan Ellenberg, Wanlin Li
The Ceresa cycle is an algebraic cycle attached to a smooth algebraic curve with a marked point, which is trivial when the curve is hyperelliptic with a marked Weierstrass point. T…
Tropical curves of hyperelliptic type
Daniel Corey
We introduce the notion of tropical curves of hyperelliptic type. These are tropical curves whose Jacobian is isomorphic to that of a hyperelliptic tropical curve, as polarized tro…
Tropical moduli spaces as symmetric Delta-complexes
Daniel Allcock, Daniel Corey, Sam Payne
We develop techniques for studying fundamental groups and integral singular homology of symmetric Delta-complexes, and apply these techniques to study moduli spaces of stable tropi…
Initial degenerations of Grassmannians
Daniel Corey
We construct closed immersions from initial degenerations of ---the open cell in the Grassmannian given by the nonvanishing o…
Khovanskii bases of Cox-Nagata rings and tropical geometry
Martha Bernal, Daniel Corey, Maria Donten-Bury +2
The Cox ring of a del Pezzo surface of degree 3 has a distinguished set of 27 minimal generators. We investigate conditions under which the initial forms of these generators genera…
Continuity properties of vectors realizing points in the classical field of values
Dan Corey, Charles R. Johnson, Ryan Kirk +2
For an -by- matrix , let be its "field of values generating function" defined as . We consider two natural versions of the continuity, whic…