Related papers: Geometric compactification of moduli spaces of hal…

Given a semisimple, compact, connected Lie group G with complexification G^c, we show there is a stable range in the homotopy type of the universal moduli space of flat connections on a principal G-bundle on a closed Riemann surface, and…

It is well known that the moduli space of flat connections on a trivial principal bundle MxG, where G is a connected Lie group, is isomorphic to the representation variety Hom(\pi_1(M), G)/G. For a tiling T, viewed as a marked copy of R^d,…

If an $m+2$-manifold $M$ is locally modeled on $\RR^{m+2}$ with coordinate changes lying in the subgroup $G=\RR^{m+2}\rtimes ({\rO}(m+1,1)\times \RR^+)$ of the affine group ${\rA}(m+2)$, then $M$ is said to be a \emph{Lorentzian similarity…

We announce the construction of toroidal partial compactifications of the moduli spaces of mixed Hodge structures with polarized graded quotients. They are moduli spaces of log mixed Hodge structures with polarized graded quotients. We…

We study equivariant localization formulas for phase space path integrals when the phase space is a multiply connected compact Riemann surface. We consider the Hamiltonian systems to which the localization formulas are applicable and show…

In this paper we investigate the existence of invariant SKT, balanced and generalized K\"ahler structures on compact quotients $\Gamma \backslash G$, where $G$ is an almost nilpotent Lie group whose nilradical has one-dimensional commutator…

The aim of these lecture notes is, after having quickly described various compactifications of the Teichm\"{u}ller space of a compact connected oriented surface minus finitely many points, to give a construction, by the equivariant Gromov…

We construct absolute and relative versions of Hamiltonian Floer homology algebras for strongly semi-positive compact symplectic manifolds with convex boundary, where the ring structures are given by the appropriate versions of the…

The flow in a fixed direction on a translation surface S determines a decomposition of S into closed invariant sets, each of which is either periodic or minimal. We study this decomposition for translation surfaces in the hyperelliptic…

In this paper we study deformation classes of moduli spaces of sheaves on a projective K3 surface. More precisely, let $(S1,H1)$ and $(S2,H2)$ be two polarized K3 surfaces, $m\in\mathbb{N}$, and for $i=1,2$ let $mv_{i}$ be a Mukai vector on…

Given a $\mathfrak{g}$-action on a Poisson manifold $(M, \pi)$ and an equivariant map $J: M \rightarrow \mathfrak{h}^*,$ for $\mathfrak{h}$ a $\mathfrak{g}$-module, we obtain, under natural compatibility and regularity conditions previously…

We generalize the first author's construction of intersection spaces to the case of stratified pseudomanifolds of stratification depth 1 with twisted link bundles, assuming that each link possesses an equivariant Moore approximation for a…

There is a canonical isomorphism between the coarse moduli spaces of somooth hyperelliptic curves of genus g and binary forms of degree 2g+2 with nonzero discriminant. In this paper, we study the extension of this isomorphism to the…

We construct a relative compactification of Dolbeault moduli spaces of Higgs bundles for reductive algebraic groups on families of projective manifolds that is compatible with the Hitchin morphism.

Let ${\mathcal S^0}(H_{\gamma})$ denote the class of all univalent, harmonic, sense-preserving and normalized mappings $f$ of the unit disk $\ID$ onto the slanted half-plane $H_\gamma :=\{w:\,{\rm Re\,}(e^{i\gamma}w) >-1/2\}$ with an…

We construct non-geometric compactifications by using the F-theory dual of the heterotic string compactified on a two-torus, together with a close connection between Siegel modular forms of genus two and the equations of certain K3…

We construct universal $G$-zips on good reductions of the Pappas-Rapoport splitting models for PEL-type Shimura varieties. We study the induced Ekedahl-Oort stratification, which sheds new light on the mod $p$ geometry of splitting models.…

We introduce and study a new class of topological $G$-spaces generalizing the classical flag manifolds $G/T$ of compact connected Lie groups. These spaces, which we call the $m$-quasi-flag manifolds $ F_m = F_m(G,T) $, are topological…

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 that the moduli space of gauge equivalence classes of symplectic vortices with uniformly bounded energy in a compact Hamiltonian manifold admits a Gromov compactification by polystable vortices. This extends results of Mundet i…