Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.26525

Tropicalization and degeneration of short flag varieties and their fibers

Hannah Markwig·Michael Schlößer
View original source ↗Read source document ↗Export metadata ↓

Abstract

Tropicalizations of Grassmannians resp. flag varieties parametrizing (flags of) linear spaces have been studied intensely and reveal rich combinatorial structure. Linear degenerations of flag varieties provide ways of interpolating between products of Grassmannians and flag varieties. Tropical versions of these have been introduced recently, but their combinatorial description and computation remains a challenge. We consider a particular case which allows the use of matroidal methods, namely linear degenerate short flag varieties parametrizing tuples of linear spaces such that a projection of one is contained in the other. Their fibers turn out to be linear spaces themselves under mild assumptions, which allows a comprehensive combinatorial description of their tropicalizations, and accordingly, of tropicalizations of linear degenerate short flag varieties.

Explore related subjects

math.AG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Hannah Markwig, Michael Schlößer. 2026-09-22. Tropicalization and degeneration of short flag varieties and their fibers. https://arxiv.org/abs/2609.26525

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The Brauer-Manin obstruction for stacky curves

We show that the Brauer-Manin obstruction is the only obstruction to strong approximation for all stacky curves over global fields with finite abelian fundamental groups. This includes all stacky curves of genus $g = \frac{1}{2}$, thus explaining a recent counterexample to the Hasse principle of Bhargava-Poonen. We will furthermore show that the elementary obstruction is the only obstruction to the integral Hasse principle for smooth proper integral models of stacky curves of genus $g < 1$. We then compute the Brauer-Manin obstruction for smooth proper integral models of stacky curves of genus $\frac{1}{2}$.

math.AG↗
arXiv2026

Tropicalization of super Gromov-Witten invariants

We show that genus-0, $n$ Neveu-Schwarz marked, super Gromov-Witten invariants of a convex, toric variety $X$ can be defined and computed using tropical geometry. When $X$ is a point, the tropical, super Gromov-Witten invariants of $X$ are descendant invariants on the moduli space of tropical curves. When $X$ is a general convex, toric variety, we define a procedure that computes the tropical, inverse Euler class of the SUSY normal bundle $\overline{N}_{n, β} \rightarrow \overline{\mathcal{M}}_{0,n}(X, β)$, under the assumption that $\overline{N}_{n, β}$ is in some sense locally tropicalizable. We define the tropical, genus-0, $n$ Neveu-Schwarz marked, super Gromov-Witten invariants of $X$, and show that the definition recovers the tropical, super Gromov-Witten invariants of a point. We compute a tropical, super Gromov-Witten invariant of $\mathbb{P}^1$.

math.AG↗
arXiv2026

Optimal bounds for local volumes of threefold singularities

We establish an optimal upper bound for local volumes of Gorenstein canonical non-hypersurface threefold singularities. Specifically, we show that a klt threefold singularity with local volume at least $9$ is either a hypersurface singularity or a quotient singularity. As applications, we obtain new restrictions on the singularities of members in K-moduli spaces of Fano threefolds, and we establish a sharp inequality between local volumes and minimal log discrepancies for threefold singularities.

math.AG↗