Extension of holomorphic functions and cohomology classes from non reduced analytic subvarieties

The goal of this survey is to describe some recent results concerning the L 2 extension of holomorphic sections or cohomology classes with values in vector bundles satisfying weak semi-positivity properties. The results presented here are generalized versions of the Ohsawa-Takegoshi extension theorem, and borrow many techniques from the long series of papers by T. Ohsawa. The recent achievement that we want to point out is that the surjectivity property holds true for restriction morphisms to non necessarily reduced subvarieties, provided these are defined as zero varieties of multiplier ideal sheaves. The new idea involved to approach the existence problem is to make use of L 2 approximation in the Bochner-Kodaira technique. The extension results hold under curvature conditions that look pretty optimal. However, a major unsolved problem is to obtain natural (and hopefully best possible) L 2 estimates for the extension in the case of non reduced subvarieties -- the case when Y has singularities or several irreducible components is also a substantial issue.Comment: arXiv admin note: text overlap with arXiv:1703.00292, arXiv:1510.0523

Luminosity versus Phase-Space-Density Relation of Galaxies Revisited

We reexamined the correlation between the B-T magnitude and the phase-space-density parameter w = (D-2(25) v(o))(-1) of galaxies for the Virgo, the Coma, the Fornax, and the Perseus clusters in an effort to better understand the physical underpinning of the fundamental plane. A tight correlation (B-T = a log w + b) common to different morphological types of galaxies (E, S0, S) was found for the Virgo and the Coma clusters, with a = 1.87 +/- 0.10 and 1.33 +/- 0.11, respectively. An investigation using only E galaxies was made for the four clusters. The results indicated that the empirical linear relation might be common among the Coma, the Fornax, and the Perseus clusters, with the Virgo Cluster showing deviation. This relation, which is another way to project the fundamental plane, has an expression insensitive to the morphology and may be suitable for treating galaxies of different morphological types collectively.ArticleThe Astrophysical Journal. 531:665-675 (2000)journal articl

Large Cosmic Variance in the Clustering Properties of Lyman Alpha Emitters at z~5

We reported in a previous paper the discovery of large-scale structure of Lyman Alpha emitters (LAEs) at z=4.86+-0.03 with a projected size of 20 Mpc x 50 Mpc in narrow-band data of a 25' x 45' area of the Subaru Deep Field (Omega_0=0.3, lambda_0=0.7, H0=70 km/s/Mpc). However, the surveyed area, which corresponds to 55 Mpc x 100 Mpc, was not large enough that we can conclude that we are seeing a typical distribution of z~5 LAEs. In this Letter, we report the results of follow-up imaging of the same sky area using a new narrow-band filter (NB704, lambda_c=7046 A and FWHM=100 A) to detect LAEs at z=4.79, i.e., LAEs lying closer to us by 39 Mpc on average than the z=4.86 objects. We detect 51 LAEs at z=4.79+-0.04 down to NB704=25.7, and find that their sky distribution is quite different from the z=4.86 LAEs'. The clustering of z=4.79 LAEs is very weak on any scales and there is no large-scale high- contrast structure. The shape and the amplitude of the angular correlation function are thus largely different between the two samples. These results demonstrate a large cosmic variance in the clustering properties of LAEs on scales of ~ 50 Mpc.Comment: 4 pages (uses emulateapj5.sty), accepted for ApJ

Massive galaxies in cosmological simulations: UV-selected sample at redshift z=2

We study the properties of galaxies at z=2 in a Lambda CDM universe, using two different types of hydrodynamic simulation methods (Eulerian TVD and SPH) and a spectrophotometric analysis in the Un, G, R filter set. The simulated galaxies at z=2 satisfy the color-selection criteria proposed by Adelberger et al. (2004) when we assume Calzetti extinction with E(B-V)=0.15. We find that the number density of simulated galaxies brighter than R<25.5 at z=2 is about 2e-2 h^3/Mpc^3, roughly one order of magnitude larger than that of Lyman break galaxies at z=3. The most massive galaxies at z=2 have stellar masses >~1e11 Msun, and their observed-frame G-R colors lie in the range 0.0<G-R<1.0. They typically have been continuously forming stars with a rate exceeding 30 Msun/yr over a few Gyrs from z=10 to z=2, although the TVD simulation indicates a more sporadic star formation history than the SPH simulations. Of order half of their stellar mass was already assembled by z~4. The reddest massive galaxies at z=2 with G-R >= 1.0 and Mstar>1e10 Msun/h finished the build-up of their stellar mass by z~3. Interestingly, our study suggests that the majority of the most massive galaxies at z=2 should be detectable at rest-frame UV wavelengths, contrary to some recent claims made on the basis of near-IR studies of galaxies at the same epoch, provided the median extinction is less than E(B-V)<0.3. However, our results also suggest that the fraction of stellar mass contained in galaxies that pass the color-selection criteria could be as low as 50% of the total stellar mass in the Universe at z=2. Our simulations suggest that the missing stellar mass is contained in fainter (R>25.5) and intrinsically redder galaxies. Our results do not suggest that hierarchical galaxy formation fails to account for the massive galaxies at z>=1. (abridged)Comment: 35 pages, 11 figures. Submitted to ApJ. Error in AB magnitude calculation corrected. Higher resolution version available at http://cfa-www.harvard.edu/~knagamine/redgal.ps.g

Soft-gluon effects in WW production at hadron colliders

We consider QCD radiative corrections to WW pair production in hadron collisions. We perform a calculation that consistently combines next-to-leading order predictions with soft-gluon resummation valid at small transverse momenta ptWW of the WW pair. We present results for the ptWW distribution at the LHC up to (almost) next-to-next-to-leading logarithmic accuracy, and study the effect of resummation on the charged-lepton distributions. Soft-gluon effects are typically mild, but they can be strongly enhanced when hard cuts are applied. The relevant distributions are generally well described by the MC@NLO event generator.Comment: 15 pages, 12 postscript figures. Error corrected in NLO plot for WW transverse-mass distribution. Results unchange

Implications of the Lyman alpha Emission Line from a Candidate z=10 Galaxy

The recently discovered z=10 galaxy (Pello et al 2004) has a strong Lyman alpha emission line that is consistent with being surprisingly symmetric, even given the relatively poor quality of its spectrum. The blue wing of a Lyman alpha line originating at high redshift should be strongly suppressed by resonant hydrogen absorption along the line of sight, an expectation borne out by the observed asymmetric shapes of the existing sample of Lyman alpha emitting sources at lower redshifts (3< z < 6.7). Absorption on the blue side of the line of the Pello et al. source could be reduced if the intergalactic medium (IGM) in the vicinity of the galaxy is highly ionized, but we show that this requires an unrealistically high ionizing emissivity. We suggest instead that the Lyman alpha emitting gas be receding relative to the surrounding gas with a velocity of >= 35km/s, a large velocity that is plausible only if the galaxy is part of a larger system (group of galaxies) with a velocity dispersion >= 35km/s. We find that with this velocity shift, the observed strength and shape of the line is still consistent with the galaxy being surrounded by its own Stromgren sphere embedded in a fully neutral IGM. More generally, we predict that at any given redshift, the bright Lyman alpha emitters with broader lines would exhibit stronger asymmetry than fainter ones. Bright galaxies with symmetric Lyman alpha lines may be signposts for groups and clusters of galaxies, within which they can acquire random velocities comparable to or larger than their linewidths.Comment: 5 pages, submitted to ApJ

RAPTOR observations of delayed explosive activity in the high-redshift gamma-ray burst GRB 060206

The RAPid Telescopes for Optical Response (RAPTOR) system at Los Alamos National Laboratory observed GRB 060206 starting 48.1 minutes after gamma-ray emission triggered the Burst Alert Telescope (BAT) on-board the Swift satellite. The afterglow light curve measured by RAPTOR shows a spectacular re-brightening by ~1 mag about 1 h after the trigger and peaks at R ~ 16.4 mag. Shortly after the onset of the explosive re-brightening the OT doubled its flux on a time-scale of about 4 minutes. The total R-band fluence received from GRB 060206 during this episode is 2.3e-9 erg/cm2. In the rest frame of the burst (z = 4.045) this yields an isotropic equivalent energy release of ~0.7e50 erg in just a narrow UV band 130 +/- 22 nm. We discuss the implications of RAPTOR observations for untriggered searches for fast optical transients and studies of GRB environments at high redshift.Comment: Submitted to ApJ Letter

Fibrations of genus two on complex surfaces

We consider fibrations of genus 2 over complex surfaces. The purpose of this paper is primarily to provide a geometric description of the possible structures of the fibration on a neighborhood of a singular fiber. In particular it is shown that the "geometric data" of the singular fiber determines the fibration on its neighborhood up to a transversely holomorphic $C^{\infty}$-diffeomorphism. The method employed is quite flexible and it applies to good extent to fibrations of arbitrary genus.Comment: This is the final version, June 201

Was the Universe Reionized at Redshift 10?

Recently, Pello et al. (2004) claimed to have discovered a galaxy at a redshift z=10, and identified a feature in its spectrum with a hydrogen Lyman-alpha emission line. If this identification is correct, we show that the intergalactic medium (IGM) around the galaxy must be significantly ionized; otherwise, the damping wing of Lyman-alpha absorption by the neutral IGM would have greatly suppressed the emission line. We find either that the large-scale region surrounding this galaxy must have been largely reionized by z=10 (with a neutral fraction <0.4) or that the stars within the galaxy must be massive (>100 solar masses), and hence capable of producing a sufficiently large HII region around it. We generalize these conclusions and derive the maximum Lyman-alpha line flux for a given UV continuum flux of galaxies prior to the epoch of reionization.Comment: 12 pages, 1 figure, ApJ, submitte

The renormalization of the axial anomaly in dimensional regularization

The prescription for the $\gamma_5$-matrix within dimensional regularization in multiloop calculations is elaborated. The three-loop anomalous dimension of the singlet axial current is calculated.Comment: 11 pages, 1 figure available on request from the author, NIKHEF-H/92-1