Hodge theory and the topology of compact Kähler and complex projective manifolds
نویسنده
چکیده
1 Hodge structures 3 1.1 The Hodge decomposition . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.1 The Frölicher spectral sequence . . . . . . . . . . . . . . . . . 3 1.1.2 Hodge filtration and Hodge decomposition . . . . . . . . . . . 6 1.1.3 Hodge structures . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 Morphisms of Hodge structures . . . . . . . . . . . . . . . . . . . . . 10 1.2.1 Functoriality . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2.2 Hodge classes . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.2.3 Cohomology ring . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3 Polarizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3.1 The hard Lefschetz theorem . . . . . . . . . . . . . . . . . . . 13 1.3.2 Hodge-Riemann bilinear relations . . . . . . . . . . . . . . . . 14 1.3.3 Rational polarizations . . . . . . . . . . . . . . . . . . . . . . 17
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