The purpose of this paper is to study hyperelliptic curves with extra involutions. The locus L g of such genus-g hyperelliptic curves is a g-dimensional subvariety of the moduli space of hyperelliptic curves H g . The authors present a birational parameterization of L g via dihedral invariants, and show how these invariants can be used to determine the field of moduli of points p ∈ L g . They conjecture that for p ∈ H g with | Aut(p)| > 2, the field of moduli is a field of definition, and they prove this conjecture for any point p ∈ L g such that the Klein 4-group is embedded in the reduced automorphism group of p. Further, for g = 3, they show that for every moduli point p ∈ H 3 such that | Aut(p)| > 4, the field of moduli is a field of definition. A rational model of the curve over its field of moduli is provided.

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We describe an experimental system designed for single-shot photoelectron spec-

We prove that weakly unconditionally Cauchy (w.u.C.) series and unconditionally converging (u.c.) series are preserved under the action of polynomials or holomorphic functions on Banach spaces, with natural restrictions in the latter case. Thus it is natural to introduce the unconditionally converging polynomials, defined as polynomials taking w.u.C. series into u.c. series, and analogously, the unconditionally converging holomorphic functions. We show that most of the classes of polynomials which have been considered in the literature consist of unconditionally converging polynomials. Then we study several "polynomial properties" of Banach spaces, defined in terms of relations of inclusion between classes of polynomials, and also some "holomorphic properties". We find remarkable differences with the corresponding "linear properties". For example, we show that a Banach space E has the polynomial property (V) if and only if the spaces of homogeneous scalar polynomials P( k E), k ∈ N, or the space of scalar holomorphic mappings of bounded type H b (E), are reflexive. In this case the dual space E

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Abstract. A new characterization of the Dunford-Pettis property in terms of the extensions of multilinear operators to the biduals is obtained. For the first time, multilinear characterizations of the reciprocal Dunford-Pettis property and Pe lczyński's property (V) are also found. Polynomial and holomorphic versions of these properties are given as well.

Toxoplasma gondii and Chlamydophila abortus are the 2 most common infectious causes of ovine abortion worldwide. These obligate intracellular pathogens are associated with severe placentitis leading to abortion or stillbirth in pregnant ewes, and resulting in significant economic losses. The objectives of the current study were the development, validation, and application of a duplex real-time polymerase chain reaction (PCR) assay capable of quantifying the burden of infection by T. gondii and C. abortus in material submitted for diagnostic purposes. The validation was carried out using samples from ewes experimentally infected with these organisms. Based on the numbers of genome copies detected, an arbitrary cutoff level was established to correlate with significant pathological changes sufficient to give rise to abortion. When the PCR assay was applied to samples from 66 Irish farms with naturally occurring outbreaks of ovine abortion, toxoplasmosis and enzootic abortion of ewes (EAE) accounted for 14% and 20% of the farms, respectively, while on 6% of the farms, there was evidence of dual infection. When standard diagnostic techniques including histopathological examination, serological analysis, chlamydial antigen detection, and bacteriological culture, were used on samples from the same farms, toxoplasmosis was diagnosed in 17% of farms, and EAE in 12%; dual infection was diagnosed on 3% of the farms. In general, good agreement was found between the PCR and the standard methods. The duplex real-time PCR assay developed in this study has proved to be a very sensitive and rapid tool that might provide a valuable addition to the methods currently available for routine diagnosis of ovine abortions.

Link to this article: http://journals.cambridge.org/abstract_S0305004101005175How to cite this article: MANUEL GONZÁLEZ and JOAQUÍN M. GUTIÉRREZ (2001). The Dunford-Pettis property on tensor products. AbstractWe show that, in some cases, the projective and the injective tensor products of two Banach spaces do not have the Dunford-Pettis property (DPP). As a consequence, we obtain that (c 0 ⊗ π c 0 ) * * fails the DPP. Since (c 0 ⊗ π c 0 ) * does enjoy it, this provides a new space with the DPP whose dual fails to have it. We also prove that, if E and F are L 1 -spaces, then E ⊗ F has the DPP if and only if both E and F have the Schur property. Other results and examples are given.A Banach space E has the Dunford-Pettis property (DPP, for short) if every weakly compact operator on E is completely continuous, i.e. takes weak Cauchy sequences into norm Cauchy sequences [14]. Equivalently, E has the DPP if, for all weakly null sequences (x n ) ⊂ E and (φ n ) ⊂ E * (the dual of E), we have lim φ n (x n ) = 0. If E * has the DPP, then so does E, but the converse is not true [25]. A Banach space with the Schur property has the DPP. The DPP is inherited by complemented subspaces. For more on the DPP, the reader is referred to [6,8].It was unknown for many years if the Dunford-Pettis property of E and F implies that of their projective tensor product E ⊗ π F and of their injective tensor productIt is proved in [24] that, if E and F have the DPP and contain no copy of 1 , then E ⊗ π F has both properties. It is shown in [20] that, if E and F have the Schur property, then E ⊗ F has the Schur property.Answering a question of [6], it is proved in [1] that, for compact spaces K 1 , . . . , K n , the space C(K 1 ) ⊗ π · · · ⊗ π C(K n ) has the DPP if and only if K 1 , . . . , K n are scattered.