Geometry and type IIB string theory

The derivation of the Standard Model, or supersymmetric extensions thereof, is one of the main goals of string theory model building. The present work is devoted to the study and geometrical description of type IIB superstring theory and F-theory model building. Toric geometry allows a systematic analysis of a large class of string compactification processes. Compact Calabi-Yau (CY) manifolds play a prominent role in these processes. In the last years, combinatorial methods have been worked out that permit the classification and analysis of a large number of CY varieties in terms of reflexive polyhedra. After a concise exposition of the basic concepts of toric geometry, we study the so-called Large Volume Scenario on explicit CY manifolds. Furthermore, we systematically construct a large number of compact CY fourfolds suitable for F-theory model building. Physically motivated conditions lead to strong constraints on the geometry. We work out several examples in more detail. At the end, we focus on the complex moduli space of CY threefolds.