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We study the topology of T-duality for pairs of U(1)-bundles and three-dimensional integral cohomology classes over orbispaces. In particular, our results apply to U(1)-spaces with finite isotropy. We generalize the theory developed in our…
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…
We show how non-trivial form fields can induce an effective potential for the dilaton and metric moduli in compactifications of type II string theory and M-theory. For particular configurations, the potential can have a stable minimum. In…
The main source of inspiration for the present paper is the work of R. Rosebrugh and R.J. Wood on constructive complete distributive lattices where the authors employ elegantly the concepts of adjunction and module in their study of ordered…
We study the moduli and determine a homotopy type of the space of all generalized Morse functions on d-manifolds for given d. This moduli space is closely connected to the moduli space of all Morse functions studied in the paper…
We introduce the notion of topological hyperbolicity to characterize the largeness of the topological fundamental group of a complex variety. Inspired by the Shafarevich conjecture, we propose to study the topological hyperbolicity of…
We introduce the notion of being cohomologically complete for objects of the derived category of sheaves of $Z[\hbar]$-modules on a topological space. Then we consider a $Z[\hbar]$-algebra satisfying some suitable conditions and prove…
Cone spherical surfaces are orientable Riemannian surfaces with constant curvature one and a finite set of conical singularities. A subset of these surfaces, referred to as dihedral surfaces, is characterized by their monodromy groups,…
In this talk I shall try to give an elementary introduction to certain areas of mathematical physics where the idea of moduli space is used to help solve problems or to further our understanding. In the wide area of gauge theory, I shall…
The goal of this article was the S^1-equivariant transversality-problem and the compactification-problem for the moduli spaces of (perturbed) PU(2)-monopoles. A substantially improved version entitled "Moduli spaces of PU(2)-monopoles…
In this paper, we discuss the Hardy inequality with bilinear operators on general metric measure spaces. We give the characterization of weights for the bilinear Hardy inequality to hold on general metric measure spaces having polar…
Even in spaces of formal power series is required a topology in order to legitimate some operations, in particular to compute infinite summations. Many topologies can be exploited for different purposes. Combinatorists and algebraists may…
The moduli space of holomorphic fiber bundles ${\cal M}_n(\Si)$ over a compact Riemann surface $\Si$ is considered. A formula for the regularised determinant and an other for the symplectic form at trivial bundle are proposed.
Given a compact pseudo-metric space, we associate to it upper and lower dimensions, depending only on the metric. Then we construct a doubling metric for which the measure of a dillated ball is closely related to these dimensions.
A moduli space ${\mathcal N}$ of stable parabolic vector bundles, of rank $r$ and parabolic degree zero, on a $n$-pointed curve has two naturally occurring holomorphic $T^*{\mathcal N}$--torsors over it. One of them is given by the moduli…
In this paper we study local cohomology of finitely generated bigraded modules over a standard bigraded ring with respect to the irrelevant bigraded ideals and establish a duality theorem. Several applications are considered.
In this paper we continue the study (initiated in a previous article) of linear Koszul duality, a geometric version of the standard duality between modules over symmetric and exterior algebras. We construct this duality in a very general…
We study the generalization of $R\to 1/R$ duality to arbitrary conformally invariant sigma models with an isometry. We show that any pair of dual sigma models can be represented as quotients of a self-dual sigma model obtained by gauging…
The purpose of this paper is twofold. First, we survey known results about theta dualities on moduli spaces of sheaves on curves and surfaces. Secondly, we establish new such dualities in the surface case. Among others, the case of elliptic…
Define a module representation to be a linear parameterisation of a collection of module homomorphisms over a ring. Generalising work of Knuth, we define duality functors indexed by the elements of the symmetric group of degree three…