127 research outputs found
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 ( \Msol) stars reveals filamentary and clumpy morphologies, which we quantify by means of structural indices. The FUV data are compared with X-ray, Ly, narrowband H, broadband optical/IR, and radio maps, providing a high spatial resolution atlas of star formation locales relative to the ambient hot ( K) and warm ionised ( 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 . 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
- …