New aspects of the ddc-lemma Export

@misc{citeulike:466579, abstract = {We produce examples of generalized complex structures on manifolds by generalizing results from symplectic and complex geometry. We produce generalized complex structures on symplectic fibrations over a generalized complex base. We study in some detail different invariant generalized complex structures on compact Lie groups and provide a thorough description of invariant structures on nilmanifolds, achieving a classification on 6-nilmanifolds. <br />We study implications of the `dd^c-lemma' in the generalized complex setting. Similarly to the standard dd^c-lemma, its generalized version induces a decomposition of the cohomology of a manifold and causes the degeneracy of the spectral sequence associated to the splitting d = \del + \delbar at E\_1. But, in contrast with the dd^c-lemma, its generalized version is not preserved by symplectic blow-up or blow-down (in the case of a generalized complex structure induced by a symplectic structure) and does not imply formality.}, archivePrefix = {arXiv}, author = {Cavalcanti, Gil R.}, citeulike-article-id = {466579}, citeulike-linkout-0 = {http://arxiv.org/abs/math.DG/0501406}, citeulike-linkout-1 = {http://arxiv.org/pdf/math.DG/0501406}, day = {24}, eprint = {math.DG/0501406}, keywords = {complex\_geometry, generalized\_complex\_geometry, symplectic, t-duality}, month = {Jan}, posted-at = {2006-01-17 01:59:58}, priority = {2}, title = {New aspects of the ddc-lemma}, url = {http://arxiv.org/abs/math.DG/0501406}, year = {2005} }

TY - ELEC ID - citeulike:466579 L3 - citeulike-article-id:466579 N2 - We produce examples of generalized complex structures on manifolds by generalizing results from symplectic and complex geometry. We produce generalized complex structures on symplectic fibrations over a generalized complex base. We study in some detail different invariant generalized complex structures on compact Lie groups and provide a thorough description of invariant structures on nilmanifolds, achieving a classification on 6-nilmanifolds. <br />We study implications of the `dd^c-lemma' in the generalized complex setting. Similarly to the standard dd^c-lemma, its generalized version induces a decomposition of the cohomology of a manifold and causes the degeneracy of the spectral sequence associated to the splitting d = \del + \delbar at E_1. But, in contrast with the dd^c-lemma, its generalized version is not preserved by symplectic blow-up or blow-down (in the case of a generalized complex structure induced by a symplectic structure) and does not imply formality. TI - New aspects of the ddc-lemma KW - complex_geometry KW - generalized_complex_geometry KW - symplectic KW - t-duality AU - Cavalcanti, Gil PY - 2005/Jan/24/ UR - http://arxiv.org/abs/math.DG/0501406 ER -