Related papers: Moduli spaces as ball quotients I, local theory
Projective structures on topological surfaces support the structure of 2d CFTs with a degree of technical simplification. We propose a complex analytic space $\mathcal{P}_g$ biholomorphic to $T^*_{(1,0)} \mathcal{M}_g$ as a candidate moduli…
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…
We consider modal logics of products of neighborhood frames. We define n-product of modal logics as the logic of all products of neighborhood frames of corresponding logics and find n-product of any two pretransitive Horn axiomatizable…
We investigate properties of the Hodge metric of a mixed period domain. In particular, we calculate its curvature and the curvature of the Hodge bundles. We also consider when the pull back metric via a period map is K\"ahler. Several…
The modular curves serve as excellent objects for testing conjectures in arithmetic geometry. They possess a natural geometric definition in contrast with rather nontrivial structure. On the other hand, they are well-studied from the…
A polarizable variation of Hodge structure over a smooth complex quasi projective variety $S$ is said to be defined over a number field $L$ if $S$ and the algebraic connection associated to the variation are both defined over $L$.…
In this paper we propose two guiding principles that suggest a number of conjectures (some now proved) about various forms of rigidity for moduli spaces arising in algebraic geometry. Such conjectures have group-theoretic, topological and…
We prove some semipositivity theorems for singular varieties coming from graded polarizable admissible variations of mixed Hodge structure. As an application, we obtain that the moduli functor of stable varieties is semipositive in the…
Moduli spaces of bounded local $G$-shtukas are a group-theoretic generalization of the function field analog of Rapoport and Zink's moduli spaces of $p$-divisible groups. In this article we generalize some very prominent concepts in the…
For complex connected, reductive, affine, algebraic groups $G$, we give a Lie-theoretic characterization of the semistability of principal $G$-co-Higgs bundles on the complex projective line $\mathbb{P}^1$ in terms of the simple roots of a…
This thesis is devoted to the study of algebraic cycles in projective hyper-K\"ahler manifolds and strict Calabi-Yau manifolds. It contributes to the understanding of Beauville's and Voisin's conjectures on the Chow rings of projective…
We construct (in significant generality) moduli spaces representing the functor of morphisms from a scheme into a solvable algebraic group.
A variety of local index formulas is constructed for quantum Hamiltonians with periodic boundary conditions. All dimensions of physical space as well as many symmetry constraints are covered, notably one-dimensional systems in Class DIII as…
We present two approaches to the study of the cohomology of moduli spaces of curves. Together, they allow us to compute the rational cohomology of the moduli space \Mbar_4 of stable complex curves of genus 4, with its Hodge structure.
We shall prove that a moduli space of flat irreducible Lie algebroid connections over a compact manifold has locally a natural structure of a smooth differentiable space. This is a generalization of some well known results for the moduli…
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…
This article describes some complex-analytic aspects of the moduli space of the finite-dimensional complex representations of a finite quiver, which are stable with respect to a fixed rational weight. We construct a natural structure of a…
This paper has the purpose of presenting in an organic way a new approach to integrable (1+1)-dimensional field systems and their systematic quantization emerging from intersection theory of the moduli space of stable algebraic curves and,…
We establish a ramified class field theory for smooth projective curves over local fields. As key steps in the proof, we obtain new results in the class field theory for 2-dimensional local fields of positive characteristic, and prove a…
The classical phase of the matrix model of 11-dimensional M-theory is complex, infinite-dimensional Hilbert space. As a complex manifold, the latter admits a continuum of nonequivalent, complex-differentiable structures that can be placed…