02321nam a2200409 i 4500991002946939707536m o d cr nn 008mamaa160719s2015 sz a ob 001 0 eng d978331917521810.1007/978-3-319-17521-8doib14258511-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng516.3523AMS 32G20AMS 14F05AMS 32C35AMS 53D05LC QA564.K52Kirschner, Tim716373Period mappings with applications to symplectic complex spaces[e-book] /Tim KirschnerCham :Springer,[2015]1 online resource (xviii, 275 pages)Lecture notes in mathematics,1617-9692 ;2140Includes bibliographical referencesExtending Griffiths classical theory of period mappings for compact Khler manifolds, this book develops and applies a theory of period mappings of Hodge-de Rham type for families of open complex manifolds. The text consists of three parts. The first part develops the theory. The second part investigates the degeneration behavior of the relative Frlicher spectral sequence associated to a submersive morphism of complex manifolds. The third part applies the preceding material to the study of irreducible symplectic complex spaces. The latter notion generalizes the idea of an irreducible symplectic manifold, dubbed an irreducible hyperkhler manifold in differential geometry, to possibly singular spaces. The three parts of the work are of independent interest, but intertwine nicelyGeometry, AlgebraicNumbers, ComplexSymplectic spacesCentro internazionale per la ricerca matematica <Trento, Italy>C.I.M.E. Summer School<2013 ;Levico Terme, Italy>http://link.springer.com/book/10.1007%2F978-3-319-17521-8An electronic book accessible through the Worls Wide Web.b1425851103-03-2219-07-16991002946939707536Period mappings with applications to symplectic complex spaces1388038UNISALENTOle01319-07-16m@ -engsz 00