Abstract

Many instances have recently been found on the intriguing interplay between string landscape and algebraic geometry via the swampland program. In this talk, we will exemplify such an interplay. Specifically, by addressing universal properties of compact elliptic Calabi-Yau (d+1)-folds, we will test out some of the swampland conjectures for all possible effective QFT models of F-theory in (real) D=10-2d dimensions. In particular, several results will be discussed on non-vanishing of specific enumerative invariants, as well as characterization of geometries at infinite distance in the moduli space.