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- W2481391936 abstract "LECTURE 1: Kahler manifolds, the Hodge Theorem, Lefschetz decomposition, Hodge index theorem, degeneration of the Hodge-De Rham spectral sequence, Hodge structures. LECTURE 2: Poincaré dual class of a homology cycle, cycle class of an algebraic subvariety, Griffiths intermediate Jacobian, Abel-Jacobi map, logarithmic differential forms, introduction to Deligne cohomology, infinitesimal Abel-Jacobi map. LECTURE 3: Kodaira-Spencer class, the period map and its derivative, infinitesimal period relation, Yukawa coupling, second fundamental form of the period map for curves. LECTURE 4: Poincaré residue representation of the Hodge groups of a hypersurface, pseudo-Jacobi ideal, derivative of the period map for hypersurfaces, generalized Macaulay’s theorem, infinitesimal Torelli for projective hypersurfaces and hypersurfaces of high degree, Hodge class of a complete intersection curve. LECTURE 5: Mixed Hodge structure of a quasi-projective variety, Gysin sequence and Lefschetz duality, examples of extension classes using mixed Hodge structures. LECTURE 6: Normal functions, normal function associated to a family of cycles, infinitesimal condition for normal functions, Griffiths infinitesimal invariant, normal function associated to a Deligne class. LECTURE 7: Macaulay’s lower bound on the growth of ideals, Gotzmann persistence theorem, Koszul vanishing theorem, explicit Noether-Lefschetz theorem, Donagi symmetrizer lemma, generic Torelli theorem for projective hypersurfaces, image of the Abel-Jacobi map for a general 3-fold of degree $ge 6$ , Nori’s vanishing lemma. LECTURE 8: Nori connectedness theorem and its consequences." @default.
- W2481391936 created "2016-08-23" @default.
- W2481391936 creator A5083171830 @default.
- W2481391936 date "1994-01-01" @default.
- W2481391936 modified "2023-10-17" @default.
- W2481391936 title "Infinitesimal Methods in Hodge Theory" @default.
- W2481391936 doi "https://doi.org/10.1007/978-3-540-49046-3_1" @default.
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