Period Mappings with Applications to Symplectic Complex Spaces
Kirschner, Tim.
Period Mappings with Applications to Symplectic Complex Spaces [electronic resource] / by Tim Kirschner. - 1st ed. 2015. - XVIII, 275 p. online resource. - Lecture Notes in Mathematics, 2140 0075-8434 ; . - Lecture Notes in Mathematics, 2140 .
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.
9783319175218
10.1007/978-3-319-17521-8 doi
Geometry, algebraic.
Differential equations, partial.
Algebra.
Algebraic Geometry.
Several Complex Variables and Analytic Spaces.
Category Theory, Homological Algebra.
QA564-609
516.35
Period Mappings with Applications to Symplectic Complex Spaces [electronic resource] / by Tim Kirschner. - 1st ed. 2015. - XVIII, 275 p. online resource. - Lecture Notes in Mathematics, 2140 0075-8434 ; . - Lecture Notes in Mathematics, 2140 .
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.
9783319175218
10.1007/978-3-319-17521-8 doi
Geometry, algebraic.
Differential equations, partial.
Algebra.
Algebraic Geometry.
Several Complex Variables and Analytic Spaces.
Category Theory, Homological Algebra.
QA564-609
516.35