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Period Mappings and Period Domains (Cambridge Studies in Advanced Mathematics, Series Number 85) by JAMES CARLSON, James Carlson, Stefan Müller-Stach, Chris Peters is a nonfiction available to read on EtoBox.

What is Period Mappings and Period Domains (Cambridge Studies in Advanced Mathematics, Series Number 85) about?

The Concept Of A Period Of An Elliptic Integral Goes Back To The 18th Century. Later Abel, Gauss, Jacobi, Legendre, Weierstrass And Others Made A Systematic Study Of These Integrals. Rephrased In Modern Terminology, These Give A Way To Encode How The Complex Structure Of A Two-torus Varies, Thereby Showing That Certain Families Contain All Elliptic Curves. Generalizing To Higher Dimensions Resulted In The Formulation Of The Celebrated Hodge Conjecture, And In An Attempt To Solve This, Griffiths Generalized The Classical Notion Of Period Matrix And Introduced Period Maps And Period Domains Which Reflect How The Complex Structure For Higher Dimensional Varieties Varies. The Basic Theory As Developed By Griffiths Is Explained In The First Part Of The Book. Then, In The Second Part Spectral Sequences And Koszul Complexes Are Introduced And Are Used To Derive Results About Cycles On Higher Dimensional Algebraic Varieties Such As The Noether-lefschetz Theorem And Nori's Theorem. Finally, In The Third Part Differential Geometric Methods Are Explained Leading Up To Proofs Of Arakelov-type Theorems, The Theorem Of The Fixed Part, The Rigidity Theorem, And More. Higgs Bundles And Relations T

Who reads Period Mappings and Period Domains (Cambridge Studies in Advanced Mathematics, Series Number 85)?

Author

JAMES CARLSON, James Carlson, Stefan Müller-Stach, Chris Peters

Publisher

Cambridge University Press (Virtual Publishing)

Published

2003

Language

EN

ISBN

9780521814669

Category

nonfiction

Subjects

Mathematics, Stem