Classifying Spaces of Degenerating Polarized Hodge Structures. (AM-169)

Released on by Kazuya Kato
preview-18

  • Classifying Spaces of Degenerating Polarized Hodge Structures. (AM-169) Book Detail

  • Author : Kazuya Kato
  • Release Date : 2009
  • Publisher : Princeton University Press
  • Genre : Mathematics
  • Pages : 349
  • ISBN 13 : 0691138222
  • File Size : 13,13 MB
DOWNLOAD BOOK

Classifying Spaces of Degenerating Polarized Hodge Structures. (AM-169) by Kazuya Kato PDF Summary

Book Description: In 1970, Phillip Griffiths envisioned that points at infinity could be added to the classifying space D of polarized Hodge structures. In this book, Kazuya Kato and Sampei Usui realize this dream by creating a logarithmic Hodge theory. They use the logarithmic structures begun by Fontaine-Illusie to revive nilpotent orbits as a logarithmic Hodge structure. The book focuses on two principal topics. First, Kato and Usui construct the fine moduli space of polarized logarithmic Hodge structures with additional structures. Even for a Hermitian symmetric domain D, the present theory is a refinement of the toroidal compactifications by Mumford et al. For general D, fine moduli spaces may have slits caused by Griffiths transversality at the boundary and be no longer locally compact. Second, Kato and Usui construct eight enlargements of D and describe their relations by a fundamental diagram, where four of these enlargements live in the Hodge theoretic area and the other four live in the algebra-group theoretic area. These two areas are connected by a continuous map given by the SL(2)-orbit theorem of Cattani-Kaplan-Schmid. This diagram is used for the construction in the first topic.

Disclaimer: www.yourbookbest.com does not own Classifying Spaces of Degenerating Polarized Hodge Structures. (AM-169) books pdf, neither created or scanned. We just provide the link that is already available on the internet, public domain and in Google Drive. If any way it violates the law or has any issues, then kindly mail us via contact us page to request the removal of the link.

Mumford-Tate Groups and Domains

Mumford-Tate Groups and Domains

File Size : 54,54 MB
Total View : 1859 Views
DOWNLOAD

Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This bo

Lectures on K3 Surfaces

Lectures on K3 Surfaces

File Size : 15,15 MB
Total View : 8170 Views
DOWNLOAD

K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi–Yau manifolds from various perspectives in eig

Period Mappings and Period Domains

Period Mappings and Period Domains

File Size : 5,5 MB
Total View : 5770 Views
DOWNLOAD

An introduction to Griffiths' theory of period maps and domains, focused on algebraic, group-theoretic and differential geometric aspects.