Cosmological Supergravity from a Massive Superparticle and Super Cosmological Black Holes

We describe in superspace a classical theory of two dimensional $(1,1)$ dilaton supergravity with a cosmological constant, both with and without coupling to a massive superparticle. We give general exact non-trivial superspace solutions for the compensator superfield that describes the supergravity in both cases. We then use these compensator solutions to construct models of two-dimensional supersymmetric cosmological black holes.Comment: 20 pages, Late

HST Snaphot Study of Variable Stars in Globular Clusters: Inner Region of NGC 6441

[Abridged] We present the results of a Hubble Space Telescope snapshot program to survey the inner region of the globular cluster NGC 6441 for its variable stars. A total of 57 variable stars was found including 38 RR Lyrae stars, 6 Population II Cepheids, and 12 long period variables. Of the RR Lyrae stars observed in this survey, 26 are pulsating in the fundamental mode with a mean period of 0.753d and 12 are first-overtone mode pulsators with a mean period of 0.365d. These values match up very well with those found in ground-based surveys. Combining all the available data for NGC 6441, we find mean periods of 0.759d and 0.375d for the RRab and RRc stars, respectively. We also find that the RR Lyrae in this survey are located in the same regions of a period-amplitude diagram as those found in ground-based surveys. Although NGC 6441 is a metal-rich globular cluster, its RR Lyrae more closely resemble those in Oosterhoff type II globular clusters. However, even compared to typical Oosterhoff type II systems, the mean period of its RRab stars is unusually long. We also derived I-band period-luminosity relations for the RR Lyrae stars. Of the six Population II Cepheids, five are of W Virginis type and one is a BL Herculis variable stars. This makes NGC 6441, along with NGC 6388, the most metal-rich globular cluster known to contain these types of variable stars. Another variable, V118, may also be a Population II Cepheid given its long period and its separation in magnitude from the RR Lyrae stars. We argue that there does not appear to be a change in the period-luminosity relation slope between the BL Herculis and W Virginis stars, but that a change of slope does occur when the RV Tauri stars are added to the period-luminosity relation.Comment: 28 pages, including 9 figures and 8 tables, emulateapj5/apjfonts style. Accepted by the Astronomical Journal. Approximate publication date September 2003. We recommend the interested reader to download the preprint with full-resolution figures, which can be found at http://www.astro.puc.cl/~mcatelan/Pritzl.zi

Cubic Curves, Finite Geometry and Cryptography

Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9,3,1 or 0 points of inflexion, and cubic curves are classified accordingly. The group structure and the possible numbers of rational points are also surveyed. A possible strengthening of the security of elliptic curve cryptography is proposed using a `shared secret' related to the group law. Cubic curves are also used in a new way to construct sets of points having various combinatorial and geometric properties that are of particular interest in finite Desarguesian planes.Comment: This is a version of our article to appear in Acta Applicandae Mathematicae. In this version, we have corrected a sentence in the third paragraph. The final publication is available at springerlink.com at http://www.springerlink.com/content/xh85647871215644

Representations of elementary abelian p-groups and finite subgroups of field

Suppose F is a field of prime characteristic p and E is a finite subgroup of the additive group (F,+). Then E is an elementary abelian p-group. We consider two such subgroups, say E and E', to be equivalent if there is an ? ? F× := F \ {0} such that E = ?E'. In this paper we show that rational functions can be used to distinguish equivalence classes of subgroups and, for subgroups of prime rank or rank less than twelve, we give explicit finite sets of separating invariants

A Far-UV Variability Survey of the Globular Cluster M80

We have searched for variable sources in the core region of M80, using far ultra-violet data taken with the Advanced Camera for Surveys on board the Hubble Space Telescope. We found three sources that exhibit strong signs of variability in our data. Among these is source TDK1, which we believe to be an RR Lyrae star that reached maximum brightness during our observations. The light curve shows a >3 mag FUV brightening over the course of ~5 hours, with an estimated peak brightness of ~16.7 mag, followed by a decrease to ~20 mag. Archival optical data obtained with WFPC2 confirm that TDK1 is variable in all wavebands. TDK1's SED is reasonably fit by a star with temperature T(eff)=6700K and radius R=4.2R(sun), consistent with the suggestion that it is an RR Lyrae. Based on the photometric and variability characteristics of the other two variables, we suggest that TDK2 is likely to be an SX Phoenicis star with ~55 minutes period, and TDK3 is likely another RR Lyrae. Finally, we briefly discuss the FUV counterparts to two previously known variables in M80, the classical nova T Sco and the dwarf nova DN1.Comment: 12 pages, 9 figures and 3 tables. Accepted for publication in MNRAS

On Syzygies for Rings of Invariants of Abelian Groups

It is well known that results on zero-sum sequences over a finitely generated abelian group can be translated to statements on generators of rings of invariants of the dual group. Here the direction of the transfer of information between zero-sum theory and invariant theory is reversed. First it is shown how a presentation by generators and relations of the ring of invariants of an abelian group acting linearly on a finite-dimensional vector space can be obtained from a presentation of the ring of invariants for the corresponding multiplicity free representation. This combined with a known degree bound for syzygies of rings of invariants yields bounds on the presentation of a block monoid associated to a finite sequence of elements in an abelian group. The results have an equivalent formulation in terms of binomial ideals, but here the language of monoid congruences and the notion of catenary degree is used

The Complete Solution of 2D Superfield Supergravity from graded Poisson-Sigma Models and the Super Pointparticle

Recently an alternative description of 2d supergravities in terms of graded Poisson-Sigma models (gPSM) has been given. As pointed out previously by the present authors a certain subset of gPSMs can be interpreted as "genuine" supergravity, fulfilling the well-known limits of supergravity, albeit deformed by the dilaton field. In our present paper we show that precisely that class of gPSMs corresponds one-to-one to the known dilaton supergravity superfield theories presented a long time ago by Park and Strominger. Therefore, the unique advantages of the gPSM approach can be exploited for the latter: We are able to provide the first complete classical solution for any such theory. On the other hand, the straightforward superfield formulation of the point particle in a supergravity background can be translated back into the gPSM frame, where "supergeodesics" can be discussed in terms of a minimal set of supergravity field degrees of freedom. Further possible applications like the (almost) trivial quantization are mentioned.Comment: 48 pages, 1 figure. v3: after final version, typos correcte