Period Mappings with Applications to Symplectic Complex Spaces

• Κύριος συγγραφέας: Kirschner, Tim (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Έκδοση: 1st ed. 2015.
• Σειρά: Lecture Notes in Mathematics, 2140
• Θέματα: Mathematics.; Algebraic geometry.; Category theory (Mathematics).; Homological algebra.; Functions of complex variables.; Algebraic Geometry.; Several Complex Variables and Analytic Spaces.; Category Theory, Homological Algebra.
• Φυσική περιγραφή: XVIII, 275 p. online resource.
• ISBN: 9783319175218
• ISSN: 0075-8434 ;

Extending Griffiths’ classical theory of period mappings for compact Kähler 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 Frölicher 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 hyperkähler manifold in differential geometry, to possibly singular spaces. The three parts of the work are of independent interest, but intertwine nicely.