Related papers: Tits arrangements on cubic curves

Let X be an affine variety and L be a solvable Lie subalgebra of Lie(Aut(X)) generated by a finite collection of locally finite Lie subalgebras. The authors of [arXiv:2507.09679] wondered whether L is itself locally finite. Here we present…

Simplicial arrangements are classical objects in discrete geometry. Their classification remains an open problem but there is a list conjectured to be complete at least for rank three. A further important class in the theory of hyperplane…

Given a polynomial endomorphism F of the n-dimensional affine space over a field K, we define a sequence of polynomial endomorphisms of the affine space associated to F. We call F nice if there exists an integer m such that the m-th term of…

We show that the topological classification and the smooth classification are generically the same for certain families of plane curves in a semi-local case(the double local case). Especially we give the normal form of transversely jointed…

We classify the non-degenerate homogeneous hypersurfaces in real and complex affine four-space whose symmetry group is at least four-dimensional.

We give a complete description of Lie algebras graded by an infinite irreducible locally finite root system.

Our main theorem classifies the Auslander-Reiten triangles according to properties of the morphisms involved. As a consequence, we are able to compute the mapping cone of an irreducible morphism. We finish by showing a technique for…

We study the action of the infinite Frobenius on the de Rham fundamental groups of affine curves defined over $\bfR$. As an application, we compute extension classes of real mixed Hodge structures associated with the motivic fundamental…

We describe a primary limb structure in the connectedness locus of complex cubic polynomials, where the limbs are indexed by the periodic points of the doubling map $t \mapsto 2t \ (\operatorname{mod} {\mathbb Z})$. The main renormalization…

Tits has defined Steinberg groups and Kac-Moody groups for any root system and any commutative ring R. We establish a Curtis-Tits-style presentation for the Steinberg group St of any rank > 2 irreducible affine root system, for any R.…

Under a simple assumption on Seifert surfaces, we characterise knots whose stable topological 4-genus coincides with the genus.

A commutative order in a quaternion algebra is called selective if it is embeds into some, but not all, the maximal orders in the algebra. It is known that a given quadratic order over a number field can be selective in at most one…

Trinomial hypersurfaces form a natural class of affine algebraic varieties closely connected with varieties admitting a torus action of complexity one. We investigate orbits of the automorphism group on these hypersurfaces. We prove that…

This is one of a series of papers which aims towards a classification of imprimitive affine groups of rank $3$. In this paper, a complete classification is given of such groups of characteristic $p$ such that the point stabilizer is not…

A toric arrangement is a finite collection of codimension-$1$ subtori in a torus. These subtori stratify the ambient torus into faces of various dimensions. Let $f_i$ denote the number of $i$-dimensional faces; these so-called face numbers…

The main result of the paper states that a connected complex affine algebraic curve is Lipschitz normally embedded (shortened to LNE afterwards) in $\mathbb{C}^n$ if and only if its germ at any singular point is a finite union of…

Let X be an irreducible affine T-variety. We consider families of affine stable toric T-varieties over X and give a description of the corresponding moduli space as the quotient stack of an open subscheme in a certain toric Hilbert scheme…

We classify the irreducible finite-dimensional representations of the twisted quantum affine algebras.

Let $K$ be any field with $\textup{char}K\neq 2,3$. We classify all cubic homogeneous polynomial maps $H$ over $K$ with $\textup{rk} JH\leq 2$. In particular, we show that, for such an $H$, if $F=x+H$ is a Keller map then $F$ is invertible,…

Let k be an algebraically closed field and A be a finite-dimensional associative basic k-algebra of the form A=kQ/I where Q is a quiver without oriented cycles or double arrows and I is an admissible ideal of kQ. We consider roots of the…