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Period mappings with applications to...

Kirschner, Tim.

Period mappings with applications to symplectic complex spaces

Record Type:	Electronic resources : Monograph/item
Title/Author:	Period mappings with applications to symplectic complex spacesby Tim Kirschner.
Author:	Kirschner, Tim.
Published:	Cham :Springer International Publishing :2015.
Description:	xviii, 275 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Geometry, Algebraic.
Online resource:	http://dx.doi.org/10.1007/978-3-319-17521-8
ISBN:	9783319175218$q(electronic bk.)

Period mappings with applications to symplectic complex spaces
Kirschner, Tim.

Period mappings with applications to symplectic complex spaces[electronic resource] /by Tim Kirschner. - Cham :Springer International Publishing :2015. - xviii, 275 p. :ill., digital ;24 cm. - Lecture notes in mathematics,21400075-8434 ;. - Lecture notes in mathematics ;2035..

Extending Griffiths' classical theory of period mappings for compact Kahler 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 Frolicher 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 hyperkahler manifold in differential geometry, to possibly singular spaces. The three parts of the work are of independent interest, but intertwine nicely.

ISBN: 9783319175218$q(electronic bk.)

Standard No.: 10.1007/978-3-319-17521-8doiSubjects--Topical Terms:

190843
Geometry, Algebraic.

LC Class. No.: QA564 / .K52 2015

Dewey Class. No.: 516.35

Period mappings with applications to symplectic complex spaces
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490 1 $a Lecture notes in mathematics, $x 0075-8434 ; $v 2140
520 $a Extending Griffiths' classical theory of period mappings for compact Kahler 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 Frolicher 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 hyperkahler 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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650 0 $a Numbers, Complex. $3 189550
650 0 $a Symplectic spaces. $3 731817
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Algebraic Geometry. $3 274807
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