Data Portal @ linkeddatafragments.org

Matches in Harvard for { <http://id.lib.harvard.edu/aleph/009223691/catalog> ?p ?o. }

• catalog abstract "The concept of a period of an elliptic integral goes back to the 18th century. Later Abel, Gauss, Jacobi, Legendre, Weierstrass and others made a systematic study of these integrals. Rephrased in modern terminology, these give a way to encode how the complex structure of a two-torus varies, thereby showing that certain families contain all elliptic curves. Generalizing to higher dimensions resulted in the formulation of the celebrated Hodge conjecture, and in an attempt to solve this, Griffiths generalized the classical notion of period matrix and introduced period maps and period domains which reflect how the complex structure for higher dimensional varieties varies. The basic theory as developed by Griffiths is explained in the first part of the book. Then, in the second part spectral sequences and Koszul complexes are introduced and are used to derive results about cycles on higher dimensional algebraic varieties such as the Noether-Lefschetz theorem and Nori's theorem. Finally, in the third part differential geometric methods are explained leading up to proofs of Arakelov-type theorems, the theorem of the fixed part, the rigidity theorem, and more. Higgs bundles and relations to harmonic maps are discussed, and this leads to striking results such as the fact that compact quotients of certain period domains can never admit a Kahler metric or that certain lattices in classical Lie groups can't occur as the fundamental group of a Kahler manifold.".
• catalog contributor b13004605.
• catalog contributor b13004606.
• catalog contributor b13004607.
• catalog created "c2003.".
• catalog date "2003".
• catalog date "c2003.".
• catalog dateCopyrighted "c2003.".
• catalog description "Includes bibliographical references (p. 415-425) and index.".
• catalog description "The concept of a period of an elliptic integral goes back to the 18th century. Later Abel, Gauss, Jacobi, Legendre, Weierstrass and others made a systematic study of these integrals. Rephrased in modern terminology, these give a way to encode how the complex structure of a two-torus varies, thereby showing that certain families contain all elliptic curves. Generalizing to higher dimensions resulted in the formulation of the celebrated Hodge conjecture, and in an attempt to solve this, Griffiths generalized the classical notion of period matrix and introduced period maps and period domains which reflect how the complex structure for higher dimensional varieties varies. The basic theory as developed by Griffiths is explained in the first part of the book. Then, in the second part spectral sequences and Koszul complexes are introduced and are used to derive results about cycles on higher dimensional algebraic varieties such as the Noether-Lefschetz theorem and Nori's theorem. Finally, in the third part differential geometric methods are explained leading up to proofs of Arakelov-type theorems, the theorem of the fixed part, the rigidity theorem, and more. Higgs bundles and relations to harmonic maps are discussed, and this leads to striking results such as the fact that compact quotients of certain period domains can never admit a Kahler metric or that certain lattices in classical Lie groups can't occur as the fundamental group of a Kahler manifold.".
• catalog description "pt. I. Basic Theory of the Period Map -- 1. Introductory Examples -- 2. Cohomology of Compact Kahler Manifolds -- 3. Holomorphic Invariants and Cohomology -- 4. Cohomology of Manifolds Varying in a Family -- 5. Period Maps Looked at Infinitesimally -- pt. II. The Period Map: Algebraic Methods -- 6. Spectral Sequences -- 7. Koszul Complexes and Some Applications -- 8. Further Applications: Torelli Theorems for Hypersurfaces -- 9. Normal Functions and Their Applications -- 10. Applications to Algebraic Cycles: Nori's Theorem -- pt. III. Differential Geometric Methods -- 11. Further Differential Geometric Tools -- 12. Structure of Period Domains -- 13. Curvature Estimates and Applications.".
• catalog extent "xvi, 430 p. :".
• catalog identifier "0521814669".
• catalog isPartOf "Cambridge studies in advanced mathematics ; 85".
• catalog issued "2003".
• catalog issued "c2003.".
• catalog language "eng".
• catalog publisher "Cambridge, U.K. ; New York : Cambridge University Press,".
• catalog subject "516.3/5 21".
• catalog subject "Geometry, Algebraic.".
• catalog subject "Hodge theory.".
• catalog subject "QA564 .C28 2003".
• catalog subject "Torelli theorem.".
• catalog tableOfContents "pt. I. Basic Theory of the Period Map -- 1. Introductory Examples -- 2. Cohomology of Compact Kahler Manifolds -- 3. Holomorphic Invariants and Cohomology -- 4. Cohomology of Manifolds Varying in a Family -- 5. Period Maps Looked at Infinitesimally -- pt. II. The Period Map: Algebraic Methods -- 6. Spectral Sequences -- 7. Koszul Complexes and Some Applications -- 8. Further Applications: Torelli Theorems for Hypersurfaces -- 9. Normal Functions and Their Applications -- 10. Applications to Algebraic Cycles: Nori's Theorem -- pt. III. Differential Geometric Methods -- 11. Further Differential Geometric Tools -- 12. Structure of Period Domains -- 13. Curvature Estimates and Applications.".
• catalog title "Period mappings and period domains / James Carlson, Stefan Müller-Stach, Chris Peters.".
• catalog type "text".