C-logarithmic transformations and generalized complex structures

Ryushi Goto, Kenta Hayano

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We show that there are generalized complex structures on all 4-manifolds obtained by logarithmic transformations with arbitrary multiplicity along symplectic tori with trivial normal bundle. Applying a technique of broken Lefschetz fibrations, we obtain generalized complex structures with arbitrary large numbers of connected components of type changing loci on every manifold which is obtained from a symplectic 4-manifold by a logarithmic transformation of multiplicity 0 along a symplectic torus with trivial normal bundle. Elliptic surfaces with non-zero euler characteristic and the connected sums (Formula Presented) and S1 × S3 admit twisted generalized complex structures Jn with n type changing loci for arbitrary large n.

Original languageEnglish
Pages (from-to)341-357
Number of pages17
JournalJournal of Symplectic Geometry
Issue number2
Publication statusPublished - 2016

ASJC Scopus subject areas

  • Geometry and Topology


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