相关论文: Computation of GIT quotients of semisimple groups

We construct moduli spaces of linear self-maps of projective space with marked points, up to projective equivalence. That is, we let the special linear group act simultaneously by conjugation on projective linear maps and diagonally on…

We describe CompGIT, a SageMath package to describe Geometric Invariant Theory (GIT) quotients of projective space by simple groups. The implementation is based on algorithms described by Gallardo--Martinez-Garcia--Moon--Swinarski. In…

We give explicit equations for the Chow and Hilbert quotients of a projective scheme X by the action of an algebraic torus T in an auxiliary toric variety. As a consequence we provide GIT descriptions of these canonical quotients, and…

We give an explicit approach to quotienting affine varieties by linear actions of linear algebraic groups with graded unipotent radical, using results from projective Non-Reductive GIT. Our quotients come with explicit projective…

When the action of a reductive group on a projective variety has a suitable linearisation, Mumford's geometric invariant theory (GIT) can be used to construct and study an associated quotient variety. In this article we describe how…

We construct new compactifications with good properties of moduli spaces of maps from nonsingular marked curves to a large class of GIT quotients. This generalizes from a unified perspective many particular examples considered earlier in…

Recent results in geometric invariant theory (GIT) for non-reductive linear algebraic group actions allow us to stratify quotient stacks of the form [X/H], where X is a projective scheme and H is a linear algebraic group with internally…

In the paper, we study the GIT construction of the moduli space of Chow semistable curves of genus 4 in P^3. By using the GIT method developed by Mumford and a deformation theoretic argument, we give a modular description of this moduli…

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 the locus of fixed points of a torus action on a GIT quotient of a complex vector space by a reductive complex algebraic group which acts linearly. We show that, under the assumption that $G$ acts freely on the stable locus, the…

We study GIT stability of divisors in products of projective spaces. We first construct a finite set of one-parameter subgroups sufficient to determine the stability of the GIT quotient. In addition, we characterise all maximal orbits of…

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 show that the GIT quotients of suitable loci in the Hilbert and Chow schemes of 4-canonically embedded curves of genus $g\ge 3$ are the moduli space $\bar{M}_g^{\text{ps}}$ of pseudo-stable curves constructed by Schubert in…

We generalize the classical Hilbert-Mumford criteria for GIT (semi-)stability in terms of one parameter subgroups of a linearly reductive group G over a field k, to the relative situation of an equivariant, projective morphism X -> Spec A…

The Stable Reduction Theorem guarantees that any smooth, projective, geometrically irreducible curve of genus $g \geq 2$ over a discretely valued field admits a unique stable model after a finite field extension. Computing this model is a…

We construct small desingularizations of moduli spaces of semistable quiver representations for indivisible dimension vectors using deformations of stabilites and a dimension estimate for nullcones. We apply this construction to several…

Let $X$ be a smooth projective curve over the complex numbers. We compute the Brauer group of the moduli stack of Bruhat-Tits group scheme $\mathcal{G}$-torsors on $X$. When $g(X) \geq 3$ we compute the Brauer group of the regularly stable…

In this article we review the question of constructing geometric quotients of actions of linear algebraic groups on irreducible varieties over algebraically closed fields of characteristic zero, in the spirit of Mumford's geometric…

The moduli space $\cM_g$ of nonsingular projective curves of genus $g$ is compactified into the moduli $\bcM_g$ of Deligne-Mumford stable curves of genus $g$. We compactify in a similar way the moduli space of abelian varieties by adding…

We describe the GIT compactification for the moduli space of smooth quintic surfaces in projective space. In particular, we show that a normal quintic surface with at worst an isolated double point or a minimal elliptic singularity is…