Fibrations in semi-toric and generalized complex geometry

Autor:	Cavalcanti, Gil R., Klaasse, Ralph L., Witte, Aldo
Rok vydání:	2020
Předmět:	Mathematics - Differential Geometry Mathematics - Symplectic Geometry 53D18 53D17 53D05
Zdroj:	Canadian Journal of Mathematics , Volume 75 , Issue 2 , April 2023 , pp. 645 - 685
Druh dokumentu:	Working Paper
DOI:	10.4153/S0008414X22000116
Popis:	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. Comment: 41 pages, 6 figures. Minor changes; existence on manifolds in Example 6.9 now attributed to Torres and Yazinski
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2012.13282 Zobrazit plný text záznamu View this record from Arxiv