We establish a Grothendieck–Lefschetz theorem for smooth ample subvarieties of projective varieties over an algebraically closed field characteristic zero and, more generally, whose complement has small cohomological dimension. A weaker statement is also proved in general context and all characteristics. Several applications are included.

We prove an analogue in Arakelov geometry of the Grothendieck-RiemannRoch theorem.

Convexity theory and duality theory are important issues in math- ematical programming. Within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. Furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. Finally,...