The purpose of this note is to determine the Picard group of the moduli space of vector bundles over an arbitrary algebraic surface. Since Donaldson’s pioneer work on using moduli of vector bundles to define smooth invariants of an algebraic surface, there has been a surge of interest in understanding the geometry of this moduli space. Among other things, the study of line bundles on this modul...

For any moduli space of stable representations of quivers, certain smooth varieties, compactifying projective space fibrations over the moduli space, are constructed. The boundary of this compactification is analyzed. Explicit formulas for the Betti numbers of the smooth models are derived. In the case of moduli of simple representations, explicit cell decompositions of the smooth models are co...

We study the natural compactification of the moduli space of branched minimal immersions of S into S. We prove that the (compactified) moduli space Md is a connected projective variety of dimension 2d+ 4. It is irreducible when d = 1, 2, and it has two irreducible components when d ≥ 3. We discuss the bubbling phenomenon at the boundary of the moduli space.

We present an exact description of the metric on the moduli space of vacua and the spectrum of massive states for four dimensional N = 2 supersymmetric SU(n) gauge theories. The moduli space of quantum vacua is identified with the moduli space of a special set of genus n − 1 hyperelliptic Riemann surfaces. 11.15.-q, 11.30.Pb Typeset using REVTEX

We study the moduli space of rank stable based instantons over a connected sum of q copies of CP. For c2 = 1 we give the homotopy type of the moduli space. For c2 = 2 we compute the cohomology of the moduli space.

We study the moduli space of instantons on a simply connected positive definite four manifold by analyzing the classifying map of the index bundle of a family of Dirac operators parametrized by the moduli space. As applications we compute the cohomology ring for the charge 2 moduli space in the rank stable limit.

We present a new compactification M(d, n) of the moduli space of self-maps of CP of degree d with n markings. It is constructed via GIT from the stable maps moduli space M0,n(CP 1 ×CP, (1, d)). We show that it is the coarse moduli space of a smooth Deligne-Mumford stack and we compute its rational Picard group.

We show that the moduli space of the (2, 0) and little-string theories compactified on T 3 with R-symmetry twists is equal to the moduli space of U(1) instantons on a noncommutative T . The moduli space of U(q) instantons on a non-commutative T 4 is obtained from little-string theories of NS5-branes at Aq−1 singularities with twists. A large class of gauge theories with N = 4 SUSY in 2+1D and N...

We establish the existence of non-constant closed geodesics on moduli spaces of SU(2) monopoles of arbitrary charge. More generally, we show that the moduli space of strongly centred monopoles of charge k, k 2, contains a totally geodesic submanifold which can be identiied with the moduli space of strongly centred 2-monopoles for even k's and with the moduli space of centred 2-monopoles for odd...

On the setting of Siegel upper half-space we study spaces bounded and vanishing mean oscillations which are defined in terms Berezin transform, use them to characterize compact Hankel operators on Bergman space. When symbols specialized be holomorphic, its corresponding Bloch space half-space.