In the theory of elliptic functions, there are two kinds of formulae of FrobeniusStickelberger [FS] and of Kiepert [K], both of which connect the function σ(u) with ℘(u) and its (higher) derivatives through determinants. These formulae are naturally generalized to hyperelliptic functions by the papers [Ô1], [Ô2], and [Ô3]. Avoiding an unneceessary generality, we restrict the story only for the ...

We show that the Fourier transform on the Jacobian of a curve interchanges " δ functions " on the curve and the theta divisor. The Torelli theorem is an immediate consequence. 1. Statement of the theorem. 1.1. We live over an algebraically closed base field k. Let J be an abelian variety equipped with a principal polarization θ : J ∼ → J • = Pic 0 (J), so we have the corresponding Fourier trans...

We prove the Prym–Green conjecture on minimal free resolutions of paracanonical curves in the case where the genus is odd.

Given a tame Galois branched cover of curves π : X → Y with any finite Galois group G whose representations are rational, we compute the dimension of the (generalized) Prym variety Prymρ(X) corresponding to any irreducible representation ρ of G. This formula can be applied to the study of algebraic integrable systems using Lax pairs, in particular systems associated with Seiberg-Witten theory. ...

Let $d(n)$ and $d^*(n)$ be, respectively, the number of divisors unitary an integer $n\geq 1.$ A divisor $d$ is to be said if it prime over $\frac{n}{d}.$ In this paper, we study mean value function $D(n)=\frac{d(n)}{d^*(n)}$ in arithmetic progressions $ \left\lbrace l+mk \mid m\in\mathbb{N}^* \text{ } (l, k)=1 \right\rbrace;$ leads back real $x\mapsto S(x;k,l)=\underset{n\equiv l[k]}{\sum\limi...

for any lacunary sequence $theta = (k_{r})$, we define the concepts of $s_{theta}-$limit point and $s_{theta}-$cluster point of a sequence of fuzzy numbers $x = (x_{k})$. we introduce the new sets  $lambda^{f}_{s_{theta}}(x)$, $gamma^{f}_{s_{theta}}(x)$ and prove some inclusion relaions between these and the sets $lambda^{f}_{s}(x)$, $gamma^{f}_{s}(x)$ introduced in ~cite{ayt:slpsfn} by aytar [...

We address issues related to (i) a proposal for resolving a long-standing tension between large volume cosmology and phenomenology as regards reconciliation of requirements of different gravitino masses within the same string-theoretic framework, as well as (ii) evaluation of soft supersymmetry breaking terms and open-string moduli masses in the context of type IIB large volume compactification...

In this article, a log del Pezzo surface of index two means a projective normal non-Gorenstein surface S such that (S, 0) is a log-terminal pair, the anti-canonical divisor −KS is ample and that 2KS is Cartier. The log del Pezzo surfaces of index two are shown to be constructed from data (X,E,∆) called fundamental triplets consisting of a non-singular rational surface X, a simple normal crossin...