Recent advances in Hodge theory: period domains, algebraic cycles, and arithmetic / ed. by M.Kerr, G.Pearlstein. - Cambridge: Cambridge university press, 2016. - xvii, 514 p.: ill. - (London Mathematical Society lecture note series; 427). - Bibliogr. at the end of the chapters. - ISBN 978-1-107-54629-5 Шифр: (Pr 1123/427) 02  Место хранения:   02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents

Preface ....................................................... vii Introduction ................................................... ix List of Conference Participants ................................ xv PART I. HODGE THEORY AT THE BOUNDARY I.A. PERIOD DOMAINS AND THEIR COMPACTIFICATIONS 1 Classical Period Domains ..................................... 3 Radu Laza and Zheng Zhang 2 The singularities of the invariant metric on the Jacobi line bundle ................................................. 45 Jose Ignacio Burgos Gil, Jurg Kramer, and Ulf Kühn 3 Symmetries of Graded Polarized Mixed Hodge Structures ....... 78 Aroldo Kaplan I.B. PERIOD MAPS AND ALGEBRAIC GEOMETRY 4 Deformation theory and limiting mixed Hodge structures ...... 88 Mark Green and Phillip Griffiths 5 Studies of closed/open mirror symmetry for quintic threefolds through log mixed Hodge theory .................. 134 Sampei Usui 6 The 14th case VHS via К3 fibrations ........................ 165 Adrian Clingher, Charles F. Doran, Jacob Lewis, Andrey Y. Novoseltsev, and Alan Thompson PART II. ALGEBRAIC CYCLES AND NORMAL FUNCTIONS 7 A simple construction of regulator indecomposable higher Chow cycles in elliptic surfaces ........................... 231 Masanori Asakura 8 A relative version of the Beilinson-Hodge conjecture ....... 241 Rob de Jeu, James D. Lewis, and Deepam Patel 9 Normal functions and spread of zero locus .................. 264 Morihiko Saito 10 Fields of definition of Hodge loci ......................... 275 Morihiko Saito and Christian Schnell 11 Tate twists of Hodge structures arising from abelian varieties .................................................. 292 Salman Abdulali 12 Some surfaces of general type for which Bloch's conjecture holds ........................................... 308 C. Pedrini and C. Weibel PART III. THE ARITHMETIC OF PERIODS III.A. MOTIVES, GALOIS REPRESENTATIONS, AND AUTOMORPHIC FORMS 13 An introduction to the Langlands correspondence ............ 333 Wushi Goldring 14 Generalized Kuga-Satake theory and rigid local systems I: the middle convolution ..................................... 368 Stefan Patrikis 15 On the fundamental periods of a motive ..................... 393 Hiroyuki Yoshida III.B. MODULAR FORMS AND ITERATED INTEGRALS 16 Geometric Hodge structures with prescribed Hodge numbers ... 414 Donu Arapura 17 The Hodge-de Rham Theory of Modular Groups ................. 422 Richard Hain