Related papers: Moduli spaces for Lam\'e functions and Abelian int…

We construct a metric simplicial complex which is an almost isometric model of the moduli space M(S) of Riemann surfaces. We then use this model to compute the "tangent cone at infinity" of M(S): it is the topological cone on the quotient…

Let $(X, \omega)$ be a compact symplectic manifold and $L$ be a Lagrangian submanifold. Suppose $(X, L)$ has a Hamiltonian $S^1$ action with moment map $\mu$. Take an invariant $\omega$-compatible almost complex structure, we consider…

We prove results about orbit closures and equidistribution for the SL(2,R) action on the moduli space of compact Riemann surfaces, which are analogous to the theory of unipotent flows. The proofs of the main theorems rely on the measure…

The moduli space of abelian surfaces with polarisation of type (1,t) and a bilevel structure is of general type if t is odd and at least 17.

We compute the homotopy type of the moduli space of flat, unitary connections over aspherical surfaces, after stabilizing with respect to the rank of the underlying bundle. Over the orientable surface M^g, we show that this space has the…

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…

For any finite abelian group G, we study the moduli space of abelian $G$-covers of elliptic curves, in particular identifying the irreducible components of the moduli space. We prove that, in the totally ramified case, the moduli space has…

We construct the moduli space of r-jets at a point of Riemannian metrics on a smooth manifold. The construction is closely related to the problem of classification of jet metrics via differential invariants. The moduli space is proved to be…

We consider the moduli space of the extremal K\"ahler metrics on compact manifolds. We show that under the conditions of two-sided total volume bounds, $L^{n\over2}$-norm bounds on $\Riem$, and Sobolev constant bounds, this Moduli space can…

We study the value distribution of holomorphic curves from a general open Riemann surface into a smooth logarithmic pair $(X, D).$ By stochastic calculus, we first obtain a version of tautological inequality (proposed by McQuillan) and a…

We construct quasi-projective moduli spaces of $K$-general lattice polarized irreducible holomorphic symplectic manifolds. Moreover, we study their Baily--Borel compactification and investigate a relation between one-dimensional boundary…

Under some assumptions, we compute the Picard group of moduli of stable sheaves on Abelian surfaces. Considering relative moduli spaces, it is sufficient to consider the moduli of stable sheaves on the product of elliptic curves. By using…

We introduce a positive scalar function $\rho(a, \Omega)$ for a domain $\Omega$ of a complex manifold $X$ with a global holomorphic frame of the cotangent bundle by closed Abelian differentials, which heuristically measure the distance from…

We study moduli spaces of flat metrics on closed Riemannian orbifolds admitting such metrics. We show that for such orbifolds $\mathcal{O}$, the Teichm\"uller space of flat metrics $\mathcal{T}_{\text{flat}}(\mathcal{O})$ serves as a…

We study certain moduli spaces of stable vector bundles of rank two on cubic and quartic threefolds. In many cases under consideration, it turns out that the moduli space is complete and irreducible and a general member has vanishing…

We show that the irreducible components of any moduli space of semistable representations of a special biserial algebra are always isomorphic to products of projective spaces of various dimensions. This is done by showing that irreducible…

We use the formalism of the Bergman tau functions to study the geometry of moduli spaces of holomorphic quadratic differentials on complex algebraic curves. We introduce two natural tau functions and interpret them as holomorphic sections…

Maulik and Ranganathan have recently introduced moduli spaces of logarithmic stable pairs. We examine the theory in the case of toric surfaces, and recast the theory in this case using three ingredients: Gelfand, Kapranov and Zelevinsky…

We analyze the moduli space of non-flat homogeneous affine connections on surfaces. For Type $\mathcal{A}$ surfaces, we write down complete sets of invariants that determine the local isomorphism type depending on the rank of the Ricci…

We investigate periodic diffeomorphisms of non-compact aspherical manifolds (and orbifolds) and describe a class of spaces that have no homotopically trivial periodic diffeomorphisms. Prominent examples are moduli spaces of curves and…