Period Mappings with Applications to Symplectic Complex Spaces electronic resource by Tim Kirschner.
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TextSeries: Lecture Notes in MathematicsPublication details: Cham : Springer International Publishing : Imprint: Springer, 2015Edition: 1st ed. 2015Description: XVIII, 275 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783319175218Subject(s): mathematics | Algebraic Geometry | Category theory (Mathematics) | Homological algebra | Functions of complex variables | Mathematics | Algebraic Geometry | Several Complex Variables and Analytic Spaces | Category Theory, Homological AlgebraDDC classification: 516.35 LOC classification: QA564-609Online resources: Click here to access online
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Springer eBooksSummary: 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.
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.
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