Characteristic numbers of elliptic fourfolds

Abstract: I will first consider crepant resolutions of Weierstrass models corresponding to elliptically-fibered fourfolds with simple Lie algebras. I will further discuss the fibrations with multisections or nontrivial Mordell-Weil groups. In contrast to the case of fivefolds, Chern and Pontryagin numbers of fourfolds are invariant under crepant birational maps. This fact enables us to be able to compute Chern and Pontryagin numbers, independently from a choice of a crepant resolution, along with various other characteristic numbers such as the Euler characteristic, the holomorphic genera, the Todd-genus, the L-genus, the A-genus, and the eight-form curvature invariant from M-theory. For the case of Calabi-Yau fourfolds, F-theory compactification provides the resulting 4d N=1 gauge theories.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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