Related papers: The CompGIT package: a computational tool for Geom…
The concept of gyrogroups, with a weaker algebraic structure without associative law, was introduced under the background of $c$-ball of relativistically admissible velocities with Einstein velocity addition. A topological gyrogroup is just…
In this article, we give a survey of Geometric Invariant Theory for Toric Varieties, and present an application to the Einstein-Weyl Geometry. We compute the image of the Minitwistor space of the Honda metrics as a categorical quotient…
Given an action of a complex reductive Lie group G on a normal variety X, we show that every analytically Zariski-open subset of X admitting an analytic Hilbert quotient with projective quotient space is given as the set of semistable…
We consider actions of reductive groups on a varieties with finitely generated Cox ring, e.g., the classical case of a diagonal action on a product of projective spaces. Given such an action, we construct via combinatorial data in the Cox…
We generalize the classical semi-continuity theorem for GIT (semi)stable loci under variations of linearizations to a relative situation of an equivariant projective morphism from X to an affine base S. As an application to moduli problems,…
We study GIT quotients $X_\theta=V\!/\!\!/\!_\theta G$ whose linearisation map defines an isomorphism between the group of characters of $G$ and the Picard group of $X_\theta$ modulo torsion. Our main result establishes that the Cox ring of…
The aim of this note is to announce some results on the GIT problem for the Hilbert and Chow scheme of curves of degree d and genus g in P^{d-g}, whose full details will appear in a subsequent paper. In particular, we extend the previous…
A central question in invariant theory is that of determining the relations among invariants. Geometric invariant theory quotients come with a natural ample line bundle, and hence often a natural projective embedding. This question…
This work builds on the foundation laid by Gordon and Wilson in the study of isometry groups of solvmanifolds, i.e. Riemannian manifolds admitting a transitive solvable group of isometries. We restrict ourselves to a natural class of…
We prove that any compactified universal Jacobian over any stack of stable maps, defined using torsion-free sheaves which are Gieseker semistable with respect to a relatively ample invertible sheaf over the universal curve, admits a…
We study deformations of orbit closures for the action of a connected semisimple group $G$ on its Lie algebra $\mathfrak{g}$, especially when $G$ is the special linear group. The tools we use are on the one hand the invariant Hilbert scheme…
Given an action of a reductive group on a normal variety, we construct all invariant open subsets admitting a good quotient with a quasiprojective or a divisorial quotient space. Our approach extends known constructions like Mumford's…
When a reductive group $G$ acts linearly on a complex projective scheme $X$ there is a stratification of $X$ into $G$-invariant locally closed subschemes, with an open stratum $X^{ss}$ formed by the semistable points in the sense of…
The consistent construction of quantum field theories beyond the simplest cases requires a precise characterization of the propagating degrees of freedom. These are encoded in the single-pole structure of two-point functions, a connection…
The coadjoint representation of a connected algebraic group $Q$ with Lie algebra $\mathfrak q$ is a thrilling and fascinating object. Symmetric invariants of $\mathfrak q$ (= $\mathfrak q$-invariants in the symmetric algebra $S(\mathfrak…
We introduce Graphical Algebraic Geometry (GAG), a family of diagrammatic languages extending the Graphical Linear Algebra programme. We construct several languages within this family and prove that they are universal and complete for the…
A metric introduced on a projective space yields a homogeneous metric space known as a Cayley-Klein geometry. This construction is applicable not only to Euclidean and non-Euclidean spaces but also to kinematic spaces (space-times). A…
We investigate GIT quotients of polarized curves. More specifically, we study the GIT problem for the Hilbert and Chow schemes of curves of degree d and genus g in a projective space of dimension d-g, as the ratio v:=d/(2g-2) decreases. We…
We compute the intersection Betti numbers of the GIT model of the moduli space of Brill-Noether-Petri general curves of genus 4. This space was shown to be the final non-trivial log canonical model for the moduli space of stable genus four…
We introduce equivariant Chow-Witt groups in order to define Chow-Witt groups of quotient stacks. We compute the Chow-Witt ring of the moduli stack of stable (resp. smooth) elliptic curves, providing a geometric interpretation of the new…