Title Recent advances in Hodge theory : period domains, algebraic cycles, and arithmetic / edited by Matt Kerr, Washington University, St Louis, Gregory Pearlstein, Texas A & M University

Published Cambridge : Cambridge University Press, 2016 ©2016

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Description 1 online resource (xvii, 514 pages) : illustrations Series London Mathematical Society Lecture Note Series ; no. 427 London Mathematical Society lecture note series ; no. 427. Contents Classical period domains -- The singularities of the invariant metric on the Jacobi line bundle -- Symmetries of graded polarized mixed Hodge structures -- Deformation theory and limiting mixed Hodge structures -- Studies of closed/open mirror symmetry for quintic threefolds through log mixed Hodge theory -- The 14th case VHS via K3 fibrations -- A simple construction of regulator indecomposable higher Chow cycles in elliptic surfaces -- A relative version of the Beilinson-Hodge conjecture -- Normal functions and spread of zero locus -- Fields of definition of Hodge loci -- Tate twist of Hodge structures arising from abelian varieties -- Some surfaces of general type for which Bloch's conjecture holds -- An introduction to the Langlands correspondence -- Generalized Kuga-Satake theory and rigid local systems I: the middle convolution -- On the fundamental periods of a motive -- Geometric Hodge structures with prescribed Hodge numbers -- The Hodge-de Rham theory of modular groups Summary 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 Bibliography Includes bibliographical references Notes Print version record Subject Algebraic cycles -- Congresses Hodge theory -- Congresses Geometry, Algebraic -- Congresses Differential-algebraic equations -- Congresses MATHEMATICS -- Topology. Ecuaciones diferenciales Algebraic cycles Differential-algebraic equations Geometry, Algebraic Hodge theory Genre/Form Conference papers and proceedings Form Electronic book Author Kerr, Matthew D., 1975- editor. Pearlstein, Gregory, 1970- editor. ISBN 9781316387887 1316387887 9781316533796 1316533794 9781316532836 1316532836

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