Related papers: GIT and moduli with a twist
We introduce new invariants in equivariant birational geometry and study their relation to modular symbols and cohomology of arithmetic groups.
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…
We introduce a compact moduli scheme of marked noncommutative cubic surfaces as the GIT moduli scheme of relations of a quiver associated with a full strong exceptional collection on a cubic surface. It is a toric variety containing the…
A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.
We characterize the image of the period map for cubic fourfolds with at worst simple singularities as the complement of an arrangement of hyperplanes in the period space. It follows then that the GIT compactification of the moduli space of…
In this article, we study the geometric invariant theory (GIT) compactification of quintic threefolds. We study singularities, which arise in non-stable quintic threefolds, thus giving a partial description of the stable locus. We also give…
We construct the moduli spaces of stable maps, \bar M_g,n(P^r,d), via geometric invariant theory (GIT). This construction is only valid over Spec C, but a special case is a GIT presentation of the moduli space of stable curves of genus g…
In this paper we study the moduli spaces of nodal sextic curves. We realize each irreducible component of the GIT space of sextic curves with given number of nodes as an open subspace of type IV arithmetic quotients. We then focus on the…
It is a folklore theorem that the Kuranishi slice method can be used to construct the moduli space of semistable Higgs bundles on a closed Riemann surface as a complex space. The purpose of this paper is to provide a proof in detail. We…
We expose in detail the principle that the relative geometric invariant theory of equivariant morphisms is related to the GIT for linearizations near the boundary of the $G$-effective ample cone. We then apply this principle to construct…
We consider the action of the one-parameter subgroup of the special linear group corresponding to a simple root on Grassmannians and describe the structure of the associated Geometric Invariant Theory (GIT) quotients with respect to…
This is the authors doctoral thesis written at the Humboldt-University Berlin. It contains material from the three separate papers: "On the Kodaira dimension of the moduli space of nodal curves", "On quotients of…
By work of Looijenga and others, one has a good understanding of the relationship between GIT and Baily-Borel compactifications for the moduli spaces of degree 2 K3 surfaces, cubic fourfolds, and a few other related examples. The…
We study the moduli space of Hessian K3 surfaces as arithmetic quotients.
In this paper we build bridges between moduli theory of sheaf stable pairs on one hand and birational geometry on the other hand. We will in particular treat moduli of sheaf stable pairs on smooth projective curves in detail and present…
Let $G$ be a connected compact Lie group and let $\mathbb{G}$ be its complexification. In this paper, we establish a correspondence between the moduli spaces of holomorphic disks bounded by a $G$-invariant Lagrangian submanifold $L…
In this paper we study the moduli stack ${\mathcal U}_{1,n}^{ns}$ of curves of arithmetic genus 1 with n marked points, forming a nonspecial divisor. In arXiv:1511.03797 this stack was realized as the quotient of an explicit scheme…
We construct the Hilbert compactification of the universal moduli space of semistable vector bundles over smooth curves. The Hilbert compactification is the GIT quotient of some open part of an appropriate Hilbert scheme of curves in a…
We show for the moduli space of rank-2 coherent sheaves on an algebraic surface that there exists a 'dual' moduli space. This dual space allows a construction of the first one without using the GIT construction. Furthermore, we obtain a…
In this talk I shall try to give an elementary introduction to certain areas of mathematical physics where the idea of moduli space is used to help solve problems or to further our understanding. In the wide area of gauge theory, I shall…