Arnaud Beauville’s survey ”Vector bundles on Curves and Generalized Theta functions: Recent Results and Open Problems” [Be] appeared 10 years ago. This elegant survey is short (16 pages) but provides a complete introduction to a specific part of algebraic geometry. To repeat his succes now we need more pages, even though we assume that the reader is already acquainted with the material presente...

Abstract. Let C denote the Fermat curve over Q of prime exponent l. The Jacobian Jac(C) of C splits over Q as the product of Jacobians Jac(Ck), 1 ≤ k ≤ l−2, where Ck are curves obtained as quotients of C by certain subgroups of automorphisms of C. It is well known that Jac(Ck) is the power of an absolutely simple abelian variety Bk with complex multiplication. We call degenerate those pairs (l,...

We consider the problem of minimizing composite functions form $$f(g(x))+h(x)$$ , where f and h are convex (which can be nonsmooth) g is a smooth vector mapping. In addition, we assume that average finite number component mappings or expectation over family random mappings. propose class stochastic variance-reduced prox-linear algorithms for solving such problems bound their sample complexities...