Abstract
A stable generalized complex structure is one that is generically symplectic but degenerates along a real codimension two submanifold, where it defines a generalized Calabi–Yau structure. We introduce a formalism which allows us to view such structures as symplectic forms with singularities of logarithmic or elliptic type. This allows us to define two period maps: one for deformations in which the background 3-form flux is fixed, and one for which the flux is allowed to vary. As a result, we prove the unobstructedness of each of these deformation problems. We use the same approach to establish local classification theorems for the degeneracy locus as well as for analogues of Lagrangian submanifolds called Lagrangian branes.
| Original language | English |
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| Pages (from-to) | 1075-1111 |
| Number of pages | 37 |
| Journal | Proceedings of the London Mathematical Society |
| Volume | 116 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 1 May 2018 |
Funding
Received 23 March 2017; revised 2 October 2017; published online 4 December 2017. 2010 Mathematics Subject Classification 53D18 (primary), 53D05, 53D17 (secondary). G. Cavalcanti was supported by the VIDI grant number 639.032.221 from NWO, the Netherlands Organisation for Scientific Research. M.G. was supported by an NSERC Discovery Grant and acknowledges support from U.S. National Science Foundation grants DMS 1107452, 1107263, 1107367, ‘RNMS: GEometric structures And Representation varieties’ (the GEAR Network).
Keywords
- 53D05
- 53D17 (secondary)
- 53D18 (primary)