Related papers: The moduli space of 8 points on ${\bf P}^1$ and au…

We study the field of moduli of singular abelian and K3 surfaces. We discuss both the field of moduli over the CM field and over $\Q$. We also discuss non-finiteness with respect to the degree of the field of moduli. Finally, we provide an…

We construct a compactification of the moduli spaces of abelian differentials on Riemann surfaces with prescribed zeroes and poles. This compactification, called the moduli space of multi-scale differentials, is a complex orbifold with…

In this paper we prove the connectedness of isoperiodic moduli spaces of meromorphic differentials with at least three simple poles on homologically marked smooth curves whose periods are either not contained in a real line, or not…

Quaternionic tori are defined as quotients of the skew field $\mathbb{H}$ of quaternions by rank-4 lattices. Using slice regular functions, these tori are endowed with natural structures of quaternionic manifolds (in fact quaternionic…

A classical result asserts that the complex projective plane modulo complex conjugation is the 4-dimensional sphere. We generalize this result in two directions by considering the projective planes over the normed real division algebras and…

We provide a description of the moduli space of framed autodual instanton bundles on projective space, focusing on the particular cases of symplectic and orthogonal instantons. Our description will use the generalized ADHM equations which…

Let $\Lambda$ be a basic finite dimensional algebra over an algebraically closed field, presented as a path algebra modulo relations; further, assume that $\Lambda$ is graded by lengths of paths. The paper addresses the classifiability, via…

In this paper, we study the moduli space of all complex 5-dimensional Lie algebras, realizing it as a stratification by orbifolds, which are connected by jump deformations. The orbifolds are given by the action of finite groups on very…

The group PGL(3) of linear transformations of the projective plane acts naturally on the projective space parametrizing curves of a given degree. In this note we begin the study of the orbits of smooth curves under this action: we construct…

We study the geometry of some varieties of sums of powers related to the Klein quartic. This allows us to describe the birational geometry of certain moduli spaces of abelian surfaces. In particular we show that the moduli space…

Moduli spaces of complete collineations are wonderful compactifications of spaces of linear maps of maximal rank between two fixed vector spaces. We investigate the birational geometry of moduli spaces of complete collineations and quadrics…

We study the moduli space of discrete, faithful, type-preserving representations of the modular group $\mathbf{PSL}(2,\mathbb{Z})$ into $\mathbf{PU}(3,1)$. The entire moduli space $\mathcal{M}$ is a union of…

Let S be an orientable, finite type surface with negative Euler characteristic. The augmented moduli space of convex real projective structures on S was first defined and topologized by the first author. In this article, we give an explicit…

We present an approach to a large class of enumerative problems concerning rational curves in projective spaces. This approach uses analysis to obtain topological information about moduli spaces of stable maps. We demonstrate it by…

This paper further studies the matroid realization space of a specific deformation of the regular $n$-gon with its lines of symmetry. Recently, we obtained that these particular realization spaces are birational to the elliptic modular…

This paper contains detailed proofs of our results on the moduli space and the structure of noncommutative 3-spheres. We develop the notion of central quadratic form for quadratic algebras, and a general theory which creates a bridge…

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…

We construct a smooth Deligne-Mumford compactification for the moduli space of curves with an m-tuple of spin structures using line bundles on quasi-stable curves as limiting objects, as opposed to line bundles on stacky curves. For all m,…

Apart from global topological problems an affine homogeneous space is locally described by its curvature, its torsion and a slightly less tangible object called its connection in a given base point. Using this description of the local…

We prove the automorphic property of the invariant of K3 surfaces with involution, which we obtained using equivariant analytic torsion, in the case where the dimension of the moduli space is less than or equal to 2.