Brauer group of moduli spaces of pairs

We show that the Brauer group of any moduli space of stable pairs with fixed determinant over a curve is zero.Comment: 12 pages. Final version, accepted in Communications in Algebr

Moduli spaces of coherent systems of small slope on algebraic curves

Let $C$ be an algebraic curve of genus $g\ge2$. A coherent system on $C$ consists of a pair $(E,V)$, where $E$ is an algebraic vector bundle over $C$ of rank $n$ and degree $d$ and $V$ is a subspace of dimension $k$ of the space of sections of $E$. The stability of the coherent system depends on a parameter $\alpha$. We study the geometry of the moduli space of coherent systems for $0<d\le2n$. We show that these spaces are irreducible whenever they are non-empty and obtain necessary and sufficient conditions for non-emptiness.Comment: 27 pages; minor presentational changes and typographical correction

Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces

Higgs bundles and non-abelian Hodge theory provide holomorphic methods with which to study the moduli spaces of surface group representations in a reductive Lie group G. In this paper we survey the case in which G is the isometry group of a classical Hermitian symmetric space of non-compact type. Using Morse theory on the moduli spaces of Higgs bundles, we compute the number of connected components of the moduli space of representations with maximal Toledo invariant.Comment: v2: added due credits to the work of Burger, Iozzi and Wienhard. v3: corrected count of connected components for G=SU(p,q) (p \neq q); added due credits to the work of Xia and Markman-Xia; minor corrections and clarifications. 31 page

SO(p,q)-Higgs bundles and Higher Teichmuller components

Some connected components of a moduli space are mundane in the sense that they are distinguished only by obvious topological invariants or have no special characteristics. Others are more alluring and unusual either because they are not detected by primary invariants, or because they have special geometric significance, or both. In this paper we describe new examples of such 'exotic' components in moduli spaces of of SO(p, q)-Higgs bundles on closed Riemann surfaces or, equivalently, moduli spaces of surface group representations into the Lie group SO(p, q). Furthermore, we discuss how these exotic components are related to the notion of positive Anosov representations recently developed by Guichard and Wienhard. We also provide a complete count of the connected components of these moduli spaces (except for SO(2, q), with q >= 4)

Closed-Form Bayesian Inferences for the Logit Model via Polynomial Expansions

Articles in Marketing and choice literatures have demonstrated the need for incorporating person-level heterogeneity into behavioral models (e.g., logit models for multiple binary outcomes as studied here). However, the logit likelihood extended with a population distribution of heterogeneity doesn't yield closed-form inferences, and therefore numerical integration techniques are relied upon (e.g., MCMC methods). We present here an alternative, closed-form Bayesian inferences for the logit model, which we obtain by approximating the logit likelihood via a polynomial expansion, and then positing a distribution of heterogeneity from a flexible family that is now conjugate and integrable. For problems where the response coefficients are independent, choosing the Gamma distribution leads to rapidly convergent closed-form expansions; if there are correlations among the coefficients one can still obtain rapidly convergent closed-form expansions by positing a distribution of heterogeneity from a Multivariate Gamma distribution. The solution then comes from the moment generating function of the Multivariate Gamma distribution or in general from the multivariate heterogeneity distribution assumed. Closed-form Bayesian inferences, derivatives (useful for elasticity calculations), population distribution parameter estimates (useful for summarization) and starting values (useful for complicated algorithms) are hence directly available. Two simulation studies demonstrate the efficacy of our approach.Comment: 30 pages, 2 figures, corrected some typos. Appears in Quantitative Marketing and Economics vol 4 (2006), no. 2, 173--20

Supersymmetric Gauge Theories, Vortices and Equivariant Cohomology

We construct actions for (p,0)- and (p,1)- supersymmetric, 1 <= p <= 4, two-dimensional gauge theories coupled to non-linear sigma model matter with a Wess-Zumino term. We derive the scalar potential for a large class of these models. We then show that the Euclidean actions of the (2,0) and (4,0)-supersymmetric models without Wess-Zumino terms are bounded by topological charges which involve the equivariant extensions of the Kahler forms of the sigma model target spaces evaluated on the two-dimensional spacetime. We give similar bounds for Euclidean actions of appropriate gauge theories coupled to non-linear sigma model matter in higher spacetime dimensions which now involve the equivariant extensions of the Kahler forms of the sigma model target spaces and the second Chern character of gauge fields. The BPS configurations are generalisations of abelian and non-abelian vortices.Comment: 45 pages, Late

On the curvature of vortex moduli spaces

We use algebraic topology to investigate local curvature properties of the moduli spaces of gauged vortices on a closed Riemann surface. After computing the homotopy type of the universal cover of the moduli spaces (which are symmetric powers of the surface), we prove that, for genus g>1, the holomorphic bisectional curvature of the vortex metrics cannot always be nonnegative in the multivortex case, and this property extends to all Kaehler metrics on certain symmetric powers. Our result rules out an established and natural conjecture on the geometry of the moduli spaces.Comment: 25 pages; final version, to appear in Math.

Small Horizons

All near horizon geometries of supersymmetric black holes in a N=2, D=5 higher-derivative supergravity theory are classified. Depending on the choice of near-horizon data we find that either there are no regular horizons, or horizons exist and the spatial cross-sections of the event horizons are conformal to a squashed or round S^3, S^1 * S^2, or T^3. If the conformal factor is constant then the solutions are maximally supersymmetric. If the conformal factor is not constant, we find that it satisfies a non-linear vortex equation, and the horizon may admit scalar hair.Comment: 21 pages, latex. Typos corrected and reference adde

Stability Walls in Heterotic Theories

We study the sub-structure of the heterotic Kahler moduli space due to the presence of non-Abelian internal gauge fields from the perspective of the four-dimensional effective theory. Internal gauge fields can be supersymmetric in some regions of the Kahler moduli space but break supersymmetry in others. In the context of the four-dimensional theory, we investigate what happens when the Kahler moduli are changed from the supersymmetric to the non-supersymmetric region. Our results provide a low-energy description of supersymmetry breaking by internal gauge fields as well as a physical picture for the mathematical notion of bundle stability. Specifically, we find that at the transition between the two regions an additional anomalous U(1) symmetry appears under which some of the states in the low-energy theory acquire charges. We compute the associated D-term contribution to the four-dimensional potential which contains a Kahler-moduli dependent Fayet-Iliopoulos term and contributions from the charged states. We show that this D-term correctly reproduces the expected physics. Several mathematical conclusions concerning vector bundle stability are drawn from our arguments. We also discuss possible physical applications of our results to heterotic model building and moduli stabilization.Comment: 37 pages, 4 figure