Moduli spaces of irregular singular connections

In the geometric version of the Langlands correspondence, irregular singular point connections play the role of Galois representations with wild ramification. In this paper, we develop a geometric theory of fundamental strata to study irregular singular connections on the projective line. Fundamental strata were originally used to classify cuspidal representations of the general linear group over a local field. In the geometric setting, fundamental strata play the role of the leading term of a connection. We introduce the concept of a regular stratum, which allows us to generalize the condition that a connection has regular semisimple leading term to connections with non-integer slope. Finally, we construct a symplectic moduli space of meromorphic connections on the projective line that contain a regular stratum at each singular point.Comment: 53 pages. A new section (Section 4.4) has been added making precise the relationship between formal types and isomorphism classes of formal connections. Significant revisions and additions have also been made to Sections 3.1 and 4.3 and the introduction to Section

A theory of minimal K-types for flat G-bundles

The theory of minimal K-types for p-adic reductive groups was developed in part to classify irreducible admissible representations with wild ramification. An important observation was that minimal K-types associated to such representations correspond to fundamental strata. These latter objects are triples (x, r, β), where x is a point in the Bruhat-Tits building of the reductive group G, r is a nonnegative real number, and β is a semistable functional on the degree r associated graded piece of the Moy-Prasad filtration corresponding to x. Recent work on the wild ramification case of the geometric Langlands conjectures suggests that fundamental strata also play a role in the geometric setting. In this paper, we develop a theory of minimal K-types for formal flat G-bundles. We show that any formal flat G-bundle contains a fundamental stratum; moreover, all such strata have the same rational depth. We thus obtain a new invariant of a flat G-bundle called the slope, generalizing the classical definition for flat vector bundles. The slope can also be realized as the minimum depth of a stratum contained in the flat Gbundle, and in the case of positive slope, all such minimal depth strata are fundamental. Finally, we show that a flat G-bundle is irregular singular if and only if it has positive slope

Generalized serre conditions and perverse coherent sheaves

In algebraic geometry, one often encounters the following problem: given a scheme X, find a proper birational morphism Y → X where the geometry of Y is nicer than that of X. One version of this problem, first studied by Faltings, requires Y to be Cohen-Macaulay; in this case Y → X is called a Macaulayfication of X. In another variant, one requires Y to satisfy the Serre condition S r. In this paper, the authors introduce generalized Serre conditions-these are local cohomology conditions which include S r and the Cohen-Macaulay condition as special cases. To any generalized Serre condition Sρ, there exists an associated perverse t-structure on the derived category of coherent sheaves on a suitable scheme X. Under appropriate hypotheses, the authors characterize those schemes for which a canonical finite Sρ-ification exists in terms of the intermediate extension functor for the associated perversity. Similar results, including a universal property, are obtained for a more general morphism extension problem called Sρ-extension. © 2013 Elsevier Inc

Isomonodromic deformations of connections with singularities of parahoric formal type

In previous work, the authors have developed a geometric theory of fundamental strata to study connections on the projective line with irregular singularities of parahoric formal type. In this paper, the moduli space of connections that contain regular fundamental strata with fixed combinatorics at each singular point is constructed as a smooth Poisson reduction. The authors then explicitly compute the isomonodromy equations as an integrable system. This result generalizes work of Jimbo, Miwa, and Ueno to connections whose singularities have parahoric formal type.Comment: 32 pages. One of the main theorems (Theorem 5.1) has been significantly strengthened. It now states that the isomonodromy equations give rise to an integrable system on the moduli space of framed connections with fixed combinatorics instead of only on a principal GL_n bundle over this space. Sections 5 and 6 have been substantially rewritte

Dominant Nuclear Outflow Driving Mechanisms in Powerful Radio Galaxies

In order to identify the dominant nuclear outflow mechanisms in Active Galactic Nuclei, we have undertaken deep, high resolution observations of two compact radio sources (PKS 1549-79 and PKS 1345+12) with the Advanced Camera for Surveys (ACS) aboard the Hubble Space Telescope. Not only are these targets known to have powerful emission line outflows, but they also contain all the potential drivers for the outflows: relativistic jets, quasar nuclei and starbursts. ACS allows the compact nature (<0.15") of these radio sources to be optically resolved for the first time. Through comparison with existing radio maps we have seen consistency in the nuclear position angles of both the optical emission line and radio data. There is no evidence for bi-conical emission line features on the large-scale and there is a divergance in the relative position angles of the optical and radio structure. This enables us to exclude starburst driven outflows. However, we are unable to clearly distinguish between radiative AGN wind driven outflows and outflows powered by relativistic radio jets. The small scale bi-conical features, indicative of such mechanisms could be below the resolution limit of ACS, especially if aligned close to the line of sight. In addition, there may be offsets between the radio and optical nuclei induced by heavy dust obscuration, nebular continuum or scattered light from the AGN.Comment: 9 pages, 8 figures, emulateapj, ApJ Accepte

Far Ultraviolet Morphology of Star Forming Filaments in Cool Core Brightest Cluster Galaxies

We present a multiwavelength morphological analysis of star forming clouds and filaments in the central (<50 kpc) regions of 16 low redshift ($z 5$ \Msol) stars reveals filamentary and clumpy morphologies, which we quantify by means of structural indices. The FUV data are compared with X-ray, Ly$\alpha$, narrowband H$\alpha$, broadband optical/IR, and radio maps, providing a high spatial resolution atlas of star formation locales relative to the ambient hot ($\sim10^{7-8}$ K) and warm ionised ($\sim 10^4$ K) gas phases, as well as the old stellar population and radio-bright AGN outflows. Nearly half of the sample possesses kpc-scale filaments that, in projection, extend toward and around radio lobes and/or X-ray cavities. These filaments may have been uplifted by the propagating jet or buoyant X-ray bubble, or may have formed {\it in situ} by cloud collapse at the interface of a radio lobe or rapid cooling in a cavity's compressed shell. The morphological diversity of nearly the entire FUV sample is reproduced by recent hydrodynamical simulations in which the AGN powers a self-regulating rain of thermally unstable star forming clouds that precipitate from the hot atmosphere. In this model, precipitation triggers where the cooling-to- freefall time ratio is $t_{\mathrm{cool}}/t_{\mathrm{ff}}\sim 10$. This condition is roughly met at the maxmial projected FUV radius for more than half of our sample, and clustering about this ratio is stronger for sources with higher star formation rates

First-Year Spectroscopy for the SDSS-II Supernova Survey

This paper presents spectroscopy of supernovae discovered in the first season of the Sloan Digital Sky Survey-II Supernova Survey. This program searches for and measures multi-band light curves of supernovae in the redshift range z = 0.05 - 0.4, complementing existing surveys at lower and higher redshifts. Our goal is to better characterize the supernova population, with a particular focus on SNe Ia, improving their utility as cosmological distance indicators and as probes of dark energy. Our supernova spectroscopy program features rapid-response observations using telescopes of a range of apertures, and provides confirmation of the supernova and host-galaxy types as well as precise redshifts. We describe here the target identification and prioritization, data reduction, redshift measurement, and classification of 129 SNe Ia, 16 spectroscopically probable SNe Ia, 7 SNe Ib/c, and 11 SNe II from the first season. We also describe our efforts to measure and remove the substantial host galaxy contamination existing in the majority of our SN spectra.Comment: Accepted for publication in The Astronomical Journal(47pages, 9 figures