Translation surfaces arise in complex analysis, the classification of surface diffeomorphisms and the study of polygonal billiards. In recent years there have been some notable advances in understanding their properties. In particular Calta and McMullen have made significant advances in understanding translation structures in genus 2. This paper is motivated by our desire to reformulate and ext...

Results of Beauville imply that Zα is finite dimensional (cf. 2.5 below). In case A = J(C), the jacobian of a curve C, Ceresa has shown that the cycle C−C := C−(−1)∗C ∈ ZC is not algebraically equivalent to zero for generic C of genus g ≥ 3, which implies that for such a curve dimQ ZC ≥ 2. In this note we investigate the subspace ZWm of CHm(J(C))Q, with Wm the image of the m-th symmetric power ...

I t has recently been shown by Halmos [l ] that there exists a compact topological group which is algebraically isomorphic to the additive group of the real line, an example being given by the character group of the discrete additive group of the rationals. Exploiting his argument a bit further it is easy to see that the most general such example is the direct sum of N replicas of the one alrea...

We give a proof of the generalisation of Mendes-France and Van der Poorten's recent result over an arbitrary field of positive characteristic and then by extending a result of Carlitz, we shall introduce a class of algebraically independent series.

The object of the investigation is to study reducible $M$-ideals in Banach spaces. It is shown that if the number of $M$-ideals in a Banach space $X$ is $n(<infty)$, then the number of reducible $M$-ideals does not exceed of $frac{(n-2)(n-3)}{2}$. Moreover, given a compact metric space $X$, we obtain a general form of a reducible $M$-ideal in the space $C(X)$ of continuous functions on $X$. The...

In the present paper, we prove spectral mapping theorem for (m,n)-paranormal operator T on a separable Hilbert space, that is, f (?w(T)) = ?w(f(T)) when is an analytic function some open neighborhood of ?(T). We also show T, Weyl?s holds, ?(T)-?w(T) ?00(T). Moreover, if algebraically (m,n)-paranormal, then and hold.

Let X be a compact Riemann surface of genus g ≥ 2 and J(X) its Jacobian variety. By the Abel-Jacobi map X → J(X), X is embedded in J(X). The algebraic 1-cycle X −X− in J(X) is homologous to zero. Here we denote by X the image of X under the multiplication map by −1. If X is hyperelliptic, X = X in J(X). For the rest of this paper, suppose g ≥ 3. B. Harris [5] studied the problem whether the cyc...

Let G denote the full subcategory of topological abelian groups consisting of the groups that can be embedded algebraically and topologically into a product of locally compact abelian groups. We show that there is a full coreflective subcategory S of G that contains all locally compact groups and is *-autonomous. This means that for all G,H in S there is an “internal hom” G −◦H whose underlying...