Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.28028

Harder-Narasimhan Filtrations of Hyperquiver Representations

Tommi Muller
View original source ↗Read source document ↗Export metadata ↓

Abstract

Hyperquiver representations are generalisations of quiver representations. They are directed hypergraphs with vector spaces assigned to vertices, and for every directed hyperedge, an assignment of a linear map from the tensor product of the source vector spaces to the tensor product of the target vector spaces. We study the moduli of hyperquiver representations, where we use affine GIT to describe the (in)stability of such objects under the action of a product of general linear groups. Our main result introduces the Harder-Narasimhan filtration of a hyperquiver representation. We also derive a formula for the weights of this unique filtration, which specialise to the Harder-Narasimhan slopes of a quiver representation.

Explore related subjects

math.AGmath.RT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Tommi Muller. 2026-10-20. Harder-Narasimhan Filtrations of Hyperquiver Representations. https://arxiv.org/abs/2610.28028

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

KEEP EXPLORING

Related papers

arXiv2026

Automorphisms of Plane Curves defined from Chebychev polynomials

For any $d\geq 4$ we determine the automorphism groups of the algebraic curves \[ \mathcal{C}_d : y^d = φ_d(x), \] where $φ_d(x)$ denotes the Chebyshev polynomial of degree $d$, defined over a field $k$ with $p:=\operatorname{char}(k) \nmid 2d$. For $d>4$, it is $\mathbb{Z}/d\mathbb{Z}\times\mathbb{Z}/2\mathbb{Z}$, except when $2d=p^r+1$ or $4d=p^r+1$ for some $r\geq 1$. In these cases it is, respectively, $(\mathbb{Z}/d\mathbb{Z}\times\mathbb{Z}/d\mathbb{Z})\rtimes S_3$ and $\mathbb{Z}/d\mathbb{Z}\times S_3$. Two ingredients used here are a description of all total inflection points on $\cC_d$, and knowledge of the group of fractional linear transformations that preserve the set of zeros of $φ_d$.

math.AG↗
arXiv2026

On the complement of nef divisors on projective manifolds

Let $X'$ be a complex projective manifold, $\dim X'>1$, $Z$ a connected analytic subset of codimension one which is the support of a nef effective Cartier divisor $D$ on $X'$, $X:=X'\setminus Z$. Let $κ(D)$ be the Iitaka dimension of $D$. We prove that $X$ is not Hartogs if and only if $D$ is abundant and $κ(D)=1$. In particular, $X$ is not Hartogs if and only if $X$ is a proper fibration over an affine curve.

math.AG↗
arXiv2026

Tiny and Unique: The Lubin-Tate Action at Height $p-1$ from the Minimal Curve with Its Symmetries

Let $p$ be odd and $G' = \mathbb{Z}/p \rtimes \mathbb{Z}/(p-1)^2$ the maximal finite subgroup of the Morava stabilizer group at height $p-1$. Inverse Galois theory produces from $G'$ alone a curve $X$, the unique curve of minimal genus with $\operatorname{Aut}(X) \simeq G'$; its ramification, its field of definition and its equation are consequences of the group, not choices. We prove a $G'$-equivariant equivalence between the deformations of $X$ and Lubin--Tate space, so that the Lubin--Tate action of $G'$ is the action of $\operatorname{Aut}(X)$ on deformations of the curve. The proof is a coordinate-free Kodaira--Spencer argument reducing to a single character count. The action becomes explicit: $G'$ acts through $\mathbb{F}_p \rtimes \mathbb{F}_p^\times$ shifting and scaling $p+1$ points on $\mathbb{P}^1$. From this we compute $H^*(G', π_* E_{p-1})$ and its Tate cohomology. One identity, $π^{p-1} = -p$, runs through every section.

math.AG↗