Recent Advances in Hodge Theory (eBook, PDF)

Period Domains, Algebraic Cycles, and Arithmetic
Redaktion: Kerr, Matt

• Format: PDF

Produktbeschreibung

In its simplest form, Hodge theory is the study of periods - integrals of algebraic differential forms which arise in the study of complex geometry and moduli, number theory and physics. Organized around the basic concepts of variations of Hodge structure and period maps, this volume draws together new developments in deformation theory, mirror symmetry, Galois representations, iterated integrals, algebraic cycles and the Hodge conjecture. Its mixture of high-quality expository and research articles make it a useful resource for graduate students and seasoned researchers alike.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 4. Februar 2016
• Englisch
• ISBN-13: 9781316532355
• Artikelnr.: 44758703

Inhaltsangabe

Preface Matt Kerr and Gregory Pearlstein; Introduction Matt Kerr and
Gregory Pearlstein; List of conference participants; Part I. Hodge Theory
at the Boundary: Part I(A). Period Domains and Their Compactifications:
Classical period domains R. Laza and Z. Zhang; The singularities of the
invariant metric on the Jacobi line bundle J. Burgos Gil, J. Kramer and U.
Kuhn; Symmetries of graded polarized mixed Hodge structures A. Kaplan; Part
I(B). Period Maps and Algebraic Geometry: Deformation theory and limiting
mixed Hodge structures M. Green and P. Griffiths; Studies of closed/open
mirror symmetry for quintic threefolds through log mixed Hodge theory S.
Usui; The 14th case VHS via K3 fibrations A. Clingher, C. Doran, A. Harder,
A. Novoseltsev and A. Thompson; Part II. Algebraic Cycles and Normal
Functions: A simple construction of regulator indecomposable higher Chow
cycles in elliptic surfaces M. Asakura; A relative version of the
Beilinson-Hodge conjecture R. de Jeu, J. D. Lewis and D. Patel; Normal
functions and spread of zero locus M. Saito; Fields of definition of Hodge
loci M. Saito and C. Schnell; Tate twists of Hodge structures arising from
abelian varieties S. Abdulali; Some surfaces of general type for which
Bloch's conjecture holds C. Pedrini and C. Weibel; Part III. The Arithmetic
of Periods: Part III(A). Motives, Galois Representations, and Automorphic
Forms: An introduction to the Langlands correspondence W. Goldring;
Generalized Kuga-Satake theory and rigid local systems I - the middle
convolution S. Patrikis; On the fundamental periods of a motive H. Yoshida;
Part III(B). Modular Forms and Iterated Integrals: Geometric Hodge
structures with prescribed Hodge numbers D. Arapura; The Hodge-de Rham
theory of modular groups R. Hain.