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Recent advances in Hodge theory : period domains, algebraic cycles, and arithmetic / [edited by] Matt Kerr and Gregory Pearlstein.

By: Contributor(s): Material type: TextTextSeries: London Mathematical Society lecture note series ; 427Publication details: Cambridge : Cambridge University Press, 2016.Description: xvii, 514 pages : illustrations ; 23 cmISBN:
  • 9781107546295
Subject(s): DDC classification:
  • 514.74 23 Su955
Contents:
pt. (I) HODGE THEORY AT THE BOUNDARY -- (I.A). PERIOD DOMAINS AND THEIR COMPACTIFICATIONS -- 1. Classical Period Domains / Zheng Zhang -- 2. The singularities of the invariant metric on the Jacobi line bundle / Ulf Kuhn -- 3. Symmetries of Graded Polarized Mixed Hodge Structures / Aroldo Kaplan -- (I.B). PERIOD MAPS AND ALGEBRAIC GEOMETRY -- 4. Deformation theory and limiting mixed Hodge structures / Phillip Griffiths -- 5. Studies of closed/open mirror symmetry for quintic threefolds through log mixed Hodge theory / Sampei Usui -- 6. The 14th case VHS via K3 fibrations / Alan Thompson -- pt. (II) ALGEBRAIC CYCLES AND NORMAL FUNCTIONS -- 7.A simple construction of regulator indecomposable higher Chow cycles in elliptic surfaces / Masanori Asakura -- 8.A relative version of the Beilinson-Hodge conjecture / Deepam Patel -- 9. Normal functions and spread of zero locus / Morihiko Saito -- 10. Fields of definition of Hodge loci / Christian Schnell -- 11. Tate twists of Hodge structures arising from abelian varieties / Salman Abdulali -- 12. Some surfaces of general type for which Bloch's conjecture holds / C. Weibel -- pt. (III) THE ARITHMETIC OF PERIODS -- (III. A). MOTIVES, GALOIS REPRESENTATIONS, AND AUTOMORPHIC FORMS -- 13. An introduction to the Langlands correspondence / Wushi Goldring -- 14. Generalized Kuga-Satake theory and rigid local systems I: the middle convolution / Stefan Patrikis -- 15. On the fundamental periods of a motive / Hiroyuki Yoshida -- (III. B). MODULAR FORMS AND ITERATED INTEGRALS -- 16. Geometric Hodge structures with prescribed Hodge numbers / Donu Arapura -- 17. The Hodge-de Rham theory of modular groups / Richard Hain.
Summary: Hodge theory lies at the heart of modern algebraic geometry and this volume explores the many contexts in which it arises, including theoretical physics. The book will be of value to graduate students and seasoned researchers alike, for its mixture of cutting-edge research and expository articles.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 514.74 Su955 (Browse shelf(Opens below)) Available 137497
Total holds: 0

Includes bibliographical references.

pt. (I) HODGE THEORY AT THE BOUNDARY --
(I.A). PERIOD DOMAINS AND THEIR COMPACTIFICATIONS --
1. Classical Period Domains / Zheng Zhang --
2. The singularities of the invariant metric on the Jacobi line bundle / Ulf Kuhn --
3. Symmetries of Graded Polarized Mixed Hodge Structures / Aroldo Kaplan --
(I.B). PERIOD MAPS AND ALGEBRAIC GEOMETRY --
4. Deformation theory and limiting mixed Hodge structures / Phillip Griffiths --
5. Studies of closed/open mirror symmetry for quintic threefolds through log mixed Hodge theory / Sampei Usui --
6. The 14th case VHS via K3 fibrations / Alan Thompson --
pt. (II) ALGEBRAIC CYCLES AND NORMAL FUNCTIONS --
7.A simple construction of regulator indecomposable higher Chow cycles in elliptic surfaces / Masanori Asakura --
8.A relative version of the Beilinson-Hodge conjecture / Deepam Patel --
9. Normal functions and spread of zero locus / Morihiko Saito --
10. Fields of definition of Hodge loci / Christian Schnell --
11. Tate twists of Hodge structures arising from abelian varieties / Salman Abdulali --
12. Some surfaces of general type for which Bloch's conjecture holds / C. Weibel --
pt. (III) THE ARITHMETIC OF PERIODS --
(III. A). MOTIVES, GALOIS REPRESENTATIONS, AND AUTOMORPHIC FORMS --
13. An introduction to the Langlands correspondence / Wushi Goldring --
14. Generalized Kuga-Satake theory and rigid local systems I: the middle convolution / Stefan Patrikis --
15. On the fundamental periods of a motive / Hiroyuki Yoshida --
(III. B). MODULAR FORMS AND ITERATED INTEGRALS --
16. Geometric Hodge structures with prescribed Hodge numbers / Donu Arapura --
17. The Hodge-de Rham theory of modular groups / Richard Hain.

Hodge theory lies at the heart of modern algebraic geometry and this volume explores the many contexts in which it arises, including theoretical physics. The book will be of value to graduate students and seasoned researchers alike, for its mixture of cutting-edge research and expository articles.

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