Related papers: Gushel-Mukai varieties: moduli

We provide a stable rationality construction for some smooth complex Gushel-Mukai varieties of dimension 6. As a consequence, we compute the integral singular cohomology of any smooth Gushel-Mukai sixfold and in particular, show that it is…

There is a well-known stratification of the moduli space $M_g$ of Deligne-Mumford stable curves of genus $g$ by the loci of stable curves with a fixed number $i$ of nodes, where $i \le 3g-3$. The associated moduli stack ${\cal M}_g$ admits…

Many moduli spaces are constructed as quotients of group actions; this paper surveys the classical theory, as well as recent progress and applications. We review geometric invariant theory for reductive groups and how it is used to…

In this paper we study the moduli stack of complexes of vector bundles (with chain isomorphisms) over a smooth projective variety $X$ via derived algebraic geometry. We prove that if $X$ is a Calabi-Yau variety of dimension $d$ then this…

The paper sets out a generalized framework for Fourier-Mukai transforms and illustrates their use via vector bundle transforms. A Fourier-Mukai transform is, roughly, an isomorphism of derived categories of (sheaves) on smooth varieties X…

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 describe three algorithms to determine the stable, semistable, and torus-polystable loci of the GIT quotient of a projective variety by a reductive group. The algorithms are efficient when the group is semisimple. By using an…

We introduce a double framing construction for moduli spaces of quiver representations. It allows us to reduce certain sheaf cohomology computations involving the universal representation, to computations involving line bundles, making them…

An ordinary Gushel-Mukai variety with a single isolated node is the intersection of the Grassmannian $G(2,5)$ with a nodal quadric and a linear space. We consider such intersections in dimension three, four and five. We describe a flop…

We describe a framework to construct tropical moduli spaces of rational stable maps to a smooth tropical hypersurface or curve. These moduli spaces will be tropical cycles of the expected dimension, corresponding to virtual fundamental…

In [arXiv:2008.04625] the authors constructed a classifying space for polystable holomorphic vector bundles on a compact K\"ahler manifold using analytic GIT theory. The aim of this article is to show that this classifying space taken in…

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 study moduli spaces of truncated local shtukas and truncated displays and describe them as concrete quotient stacks. To do this, we develop a general formalism of frames that can be applied in both cases and is also used to study…

We study Gushel-Mukai (GM) varieties of dimension 4 or 6 in characteristic $p$. Our main result is the Tate conjecture for all such varieties over finitely generated fields of characteristic $p\geq 5$. In the case of GM sixfolds, we follow…

We generalize the construction of M. Lieblich for the compactification of the moduli stack of $\PGL_r$-bundles on algebraic spaces to the moduli stack of Tanaka-Thomas $\PGL_r$-Higgs bundles on algebraic schemes. The method we use is the…

This is the first in a sequence of two articles investigating moduli stacks of global G-shtukas, which are function field analogs for Shimura varieties. Here G is a flat affine group scheme of finite type over a smooth projective curve, and…

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 article, we are going to construct arithmetic moduli stacks of $G$-bundles after our previous construction on Hodge-Iwasawa theory. These stacks parametrize certain Hodge-Iwasawa structures in a coherent way.

This article is based in part on lecture notes prepared for the summer school "The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles" at the Institute for Mathematical Sciences at the National University of Singapore in July…

We study the moduli of G-local systems on smooth but not necessarily proper complex algebraic varieties. We show that, when suitably considered as derived algebraic stacks, they carry natural Poisson structures, generalizing the well known…