Some ball quotients with a Calabi--Yau model

Recently we determined explicitly a Picard modular variety of general type. On the regular locus of this variety there are holomorphic three forms which have been constructed as Borcherds products. Resolutions of quotients of this variety, such that the zero divisors are in the branch locus, are candidates for Calabi-Yau manifolds. Here we treat one distinguished example for this. In fact we shall recover a known variety given by the equations $X_0X_1X_2=X_3X_4X_5, \,\, X_0^3+X_1^3+X_2^3=X_3^3+X_4^3+X_5^3.$ as a Picard modular variety. This variety has a projective small resolution which is a rigid Calabi-Yau manifold ($h^{12}=0$) with Euler number $72$

The modular variety of hyperelliptic curves of genus three

The modular variety of non singular and complete hyperelliptic curves with level-two structure of genus 3 is a 5-dimensional quasi projective variety which admits several standard compactifications. The first one, X, comes from the realization of this variety as a sub-variety of the Siegel modular variety of level two and genus three .We will be to describe the equations of X in a suitable projective embedding and its Hilbert function. It will turn out that X is normal. A further model comes from geometric invariant theory using so-called semistable degenerated point configurations in (P^1)^8 . We denote this GIT-compactification by Y. The equations of this variety in a suitable projective embedding are known. This variety also can by identified with a Baily-Borel compactified ball-quotient. We will describe these results in some detail and obtain new proofs including some finer results for them. We have a birational map between Y and X . In this paper we use the fact that there are graded algebras (closely related to algebras of modular forms) A,B such that X=proj(A) and Y=proj(B). This homomorphism rests on the theory of Thomae (19th century), in which the thetanullwerte of hyperelliptic curves have been computed. Using the explicit equations for $A,B$ we can compute the base locus of the map from Y to X. Blowing up the base locus and the singularity of Y, we get a dominant, smooth model {\tilde Y}. We will see that {\tilde Y} is isomorphic to the compactification of families of marked projective lines (P^1,x_1,...,x_8), usually denoted by {\bar M_{0,8}}. There are several combinatorial similarities between the models X and Y. These similarities can be described best, if one uses the ball-model to describe Y.Comment: 39 page

Some Siegel threefolds with a Calabi-Yau model II

In the paper [FSM] we described some Siegel modular threefolds which admit a Calabi-Yau model. Using a different method we give in this paper an enlarged list of such varieties that admits a Calabi-Yau model in the following weak sense: there exists a desingularization in the category of complex spaces of the Satake compactification which admits a holomorphic three-form without zeros and whose first Betti number vanishes Basic for our method is the paper [GN] of van Geemen and Nygaard.Comment: 23 pages, no figure

A Siegel cusp form of degree 12 and weight 12

The theta series of the two unimodular even positive definite lattices of rank 16 are known to be linearly dependent in degree at most 3 and linearly independent in degree 4. In this paper we consider the next case of the 24 Niemeier lattices of rank 24. The associated theta series are linearly dependent in degree at most 11 and linearly independent in degree 12. The resulting Siegel cusp form of degree 12 and weight 12 is a Hecke eigenform which seems to have interesting properties.Comment: 12 pages, plain te

The partnership: Space shuttle, space science, and space station

An overview of the NASA Space Station Program functions, design, and planned implementation is presented. The discussed functions for the permanently manned space facility include: (1) development of new technologies and related commercial products; (2) observations of the Earth and the universe; (3) provision of service facilities for resupply, maintenance, upgrade and repair of payloads and spacecraft; (4) provision of a transportation node for stationing, processing and dispatching payloads and vehicles; (5) provision of manufacturing and assembly facilities; (6) provision of a storage depot for parts and payloads; and (7) provision of a staging base for future space endeavors. The fundamental concept for the Space Station, as given, is that it be designed, operated, and evolved in response to a broad variety of scientific, technological, and commercial user interests. The Space Shuttle's role as the principal transportation system for the construction and maintenance of the Space Station and the servicing and support of the station crew is also discussed

Improved approximate inspirals of test-bodies into Kerr black holes

We present an improved version of the approximate scheme for generating inspirals of test-bodies into a Kerr black hole recently developed by Glampedakis, Hughes and Kennefick. Their original "hybrid" scheme was based on combining exact relativistic expressions for the evolution of the orbital elements (the semi-latus rectum p and eccentricity e) with approximate, weak-field, formula for the energy and angular momentum fluxes, amended by the assumption of constant inclination angle, iota, during the inspiral. Despite the fact that the resulting inspirals were overall well-behaved, certain pathologies remained for orbits in the strong field regime and for orbits which are nearly circular and/or nearly polar. In this paper we eliminate these problems by incorporating an array of improvements in the approximate fluxes. Firstly, we add certain corrections which ensure the correct behaviour of the fluxes in the limit of vanishing eccentricity and/or 90 degrees inclination. Secondly, we use higher order post-Newtonian formulae, adapted for generic orbits. Thirdly, we drop the assumption of constant inclination. Instead, we first evolve the Carter constant by means of an approximate post-Newtonian expression and subsequently extract the evolution of iota. Finally, we improve the evolution of circular orbits by using fits to the angular momentum and inclination evolution determined by Teukolsky based calculations. As an application of the improved scheme we provide a sample of generic Kerr inspirals and for the specific case of nearly circular orbits we locate the critical radius where orbits begin to decircularise under radiation reaction. These easy-to-generate inspirals should become a useful tool for exploring LISA data analysis issues and may ultimately play a role in source detection.Comment: 25 pages, 14 figures, some typos corrected, short section on conservative corrections added, minor changes for consistency with published versio

Modular forms on SU(2,1) with weight 1/3

In this note, we describe several new examples of holomorphic modular forms on the group SU(2,1). These forms are distinguished by having weight 13. We also describe a method for determining the levels at which one should expect to find such fractional weight forms

The modular variety of hyperelliptic curves of genus three

The modular variety of nonsingular and complete hyperelliptic curves with level-two structure of genus 3 is a 5-dimensional quasi-projective variety which admits several standard compactifications. The first one realizes this variety as a subvariety of the Siegel modular variety of level two and genus three. It has 36 irreducible (isomorphic) components. One of the purposes of this paper will be to describe the equations of one of these components. Two further models use the fact that hyperelliptic curves of genus three can be obtained as coverings of a projective line with 8 branch points. There are two important compactifications of this configuration space. The first one, Y, uses the semistable degenerated point configurations in (P(1))(8). This variety also can be identified with a Baily-Borel compactified ball-quotient Y = (B/Gamma[1 - i]) over bar. We will describe these results in some detail and obtain new proofs including some finer results for them. The other compactification uses the fact that families of marked projective lines can degenerate to stable marked curves of genus 0. We use the standard notation (M) over bar (0,8) for this compactification. We have a diagram [GRAPHICS] The horizontal arrow is only birational but not everywhere regular. In this paper we find another realization of this triangle which uses the fact that there are graded algebras (closely related to algebras of modular forms) A, B such that X = proj(A), Y = proj(B)

WHOI acoustic telemetry project interim report 12/1/88 - 6/1/89

This interim report covers the progress of the acoustic telemetry project during the period 12/1/88 to 5/15/89. In general, the work followed the format specified in WHOI proposal No. 5674.1. The major exception was the deletion of the transmitter array development task and a corresponding funding decrease from $242,242 to$170,000. In addition, the period for the funding was extended to June 30, partly due to a two month delay in project startup. The telemetry project was centered around the construction, programming and testing of a digital receiver prototype capable of supporting future signal processing algorithms in real-time over ocean acoustic channels. The baseline receiver consists of a two-channel analog quadrature demodulator, and interface to a multiprocessor receiver for digital signal processing. The software developed includes routines for command and control of the analog demodulator, data handling and formatting, and minimal software to digitally implement an incoherent MFSK demodulator, synchronizer and data decoder. Data storage and display programs were also completed to facilitate the performance analysis of the unit during testing. The system was tested in Woods Hole harbor at data rates up to 4800 bits/sec. The acoustic channel was time-dispersive Rayleigh fading, and performance close to theoretical expectations was achieved. We are confident that the system error behavior is arising from channel-caused effects and known deficiencies in system performance, such as excessive synchronizer steady-state jitter.Funding was provided by the Office of Naval Research under contract Number N00014-86-K-0751, and by the Charles Stark Draper Laboratory Inc

In vivo analysis of staphylococcus aureus-infected mice reveals differential temporal and spatial expression patterns of fhuD2

Staphylococcus aureus is an opportunistic human pathogen and a major cause of invasive infections such as bacteremia, endocarditis, pneumonia and wound infections. FhuD2 is a staphylococcal lipoprotein involved in the uptake of iron-hydroxymate and is under the control of the iron uptake regulator Fur. The protein is part of an investigational multi-component vaccine formulation that has shown protective efficacy in several murine models of infection. Even though fhuD2 expression was shown to be upregulated in murine kidneys infected with S. aureus, it is unknown whether the bacterium undergoes increased iron deprivation during prolonged infection. Furthermore, different infection niches of S. aureus might provide different environments and iron availability resulting in different fhuD2 expression pattern within different host organs. To address these questions, we characterized the in vitro expression of the fhuD2 gene and confirmed Fur-dependent iron-regulation of its expression. We further investigated its expression in mice infected with a bioluminescent reporter strain of S. aureus expressing the luciferase operon under the control of the fhuD2 promoter. The emission of bioluminescence in different organs was followed over a seven-day time course, as well as quantitative real-time PCR analysis of the RNA transcribed from the endogenous fhuD2 gene. Using this approach, we could show that fhuD2 expression was induced during infection in all organs analyzed and that differences in expression were observed in the temporal expression profiles, and between infected organs. Our data suggest that S. aureus undergoes increased iron deprivation during progression of infection in diverse host organs and accordingly induces dedicated iron acquisition mechanisms. Since FhuD2 plays a central role in providing the pathogen with the required iron, further knowledge of the patterns of fhuD2 expression in vivo during infection is instrumental in better defining the role of this antigen in S. aureus pathogenesis and as a vaccine antigen