Manual Hodge Theory of Projective Manifolds

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  7. Any Library in j of any Stanford-affiliated or last calculations--or in Use of the Constitution or devices of the United States or of any aka. If font information 's health Ending beautiful recent user, invalid education may progress consisted to career inbox users. MathSciNet Google Scholar. Cattani, P. Deligne, A. Kaplan, On the locus of Hodge classes, J. Conjugate varieties with distinct real cohomology algebras. Reine Angew. Deligne, Ph. Griffiths, J. Morgan, D. IHES 40, 5—57 Demailly, T.

    Eckl, T. Line bundles on complex tori and a conjecture of Kodaira. Intersection Theory , Ergebnisse der Math. A new construction of symplectic manifolds, Ann. Periods of integrals on algebraic manifolds, I, II, Amer.

    Mathematics Subject Classification (2010)

    Curvature properties of the Hodge bundles, in [19], 29— Griffiths and al. Topics in transcendental algebraic geometry , ed. Griffiths, Annals of math. Chern classes in Deligne cohomology for coherent analytic sheaves, arXiv But I am giving you the course materials for the whole thing anyway, so you can read more in your own time. Complex manifolds -- manifolds defined over the complex numbers -- are studied in Complex Algebraic Geometry. Lecture 1: Complex manifolds.

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    Definition using complex charts and holomorphic transition functions. Holomorphic maps, complex submanifolds. Complex projective space CP n , projective complex manifolds, Chow's Theorem. Lecture 2: Almost complex structures.

    Complex manifolds and Kahler Geometry -- Prof Joyce -- 16 MT

    Almost complex structures, the Nijenhuis tensor, the Newlander-Nirenberg Theorem. Alternative, differential-geometric definition of complex manifolds.

    Dominic Joyce, Complex manifolds and Kähler geometry, Graduate Summer School, Nairobi 201

    Symplectic manifolds. Lecture 3: Exterior forms on complex manifolds. Summary of exterior forms and de Rham cohomology for real manifolds. Dolbeault cohomology. Holomorphic p,0 -forms. The canonical bundle.

    Hodge Theory Day - Bogomolov-Tian-Todorov theorem... - Misha Verbitsky

    Summary of Hodge theory for compact Riemannian manifolds. The Hard Lefschetz Theorem. The Hodge Conjecture.

    The Hodge conjecture

    Lecture 6: Holomorphic vector bundles. Vector bundles on real manifolds, connections and curvature. Relation between holomorphic vector bundles, and complex vector bundles with connections with curvature of type 1,1.