Singular Fibers and Coulomb Phases

摘要

Crepant resolutions of singular elliptic fibrations play an important role in M- and F-theory compactifications on elliptically fibered Calabi-Yau fourfolds. Of particular relevance is the structure of fibers in codimension two and three, which do not necessarily fall into the Kodaira classification that is applicable in codimension one. We present a method, inspired by three-dimensional N= 2 gauge theories and their classical Coulomb branch, in order to systematically describe the fibers in higher codimension and provide a characterization in terms of representation theoretic data, much like the Kodaira classification in terms of affine Dynkin diagrams for the ADE type singular fibers.