Recent Advances in Hodge Theory
Period Domains, Algebraic Cycles, and Arithmetic

Combines cutting-edge research and expository articles in Hodge theory. An essential reference for graduate students and researchers.

Matt Kerr (Edited by), Gregory Pearlstein (Edited by)

9781107546295, Cambridge University Press

Paperback / softback, published 4 February 2016

521 pages, 10 b/w illus. 7 tables
22.8 x 15.2 x 2.8 cm, 0.73 kg

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.

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.

Subject Areas: Mathematical physics [PHU], Algebraic topology [PBPD], Algebraic geometry [PBMW], Number theory [PBH]