Geodesics and topological transitions in Calabi-Yau manifolds of Picard rank two

Abstract: We discuss the structure of the Kähler moduli space of Picard rank two Calabi-Yau threefolds, which are given in terms of complete intersections in projective ambient spaces, or as hypersurfaces in toric ambient spaces. As it turns out, flop transitions are ubiquitous in such setups. The triple intersection form of the Kähler cone generators can be brought into four different normal forms, and we use this to solve the geodesic equations in the moduli space for each one of them. Moreover, we will discuss that flops can lead to isomorphic or non-isomorphic Calabi-Yau manifolds. We find that there exist infinite flop chains of isomorphic geometries, but only a finite number of flops to inequivalent manifolds. Physically, the latter result is expected based on the swampland distance conjecture, and mathematically fits to a conjecture due to Kawamata and Morrison for Calabi-Yau threefolds.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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