Fibrations in semi-toric and generalized complex geometry
arXiv:2012.13282 · doi:10.4153/S0008414X22000116
Abstract
This paper studies the interplay between self-crossing boundary Lefschetz fibrations and generalized complex structures. We show that these fibrations arise from the moment maps in semi-toric geometry and use them to construct self-crossing stable generalized complex four-manifolds using Gompf--Thurston methods for Lie algebroids. These results bring forth further structure on several previously known examples of generalized complex manifolds. We moreover show that these fibrations are compatible with taking connected sums, and use this to prove a singularity trade result between two types of singularities occurring in these fibrations.
arXiv comment41 pages, 6 figures. Minor changes; existence on manifolds in Example 6.9 now attributed to Torres and Yazinski
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