Hodge Theory and Complex Algebraic Geometry I: Volume 1
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This is a completely self-contained modern introduction to Kaehlerian geometry and Hodge structure. The author proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. Aimed at students, the text is complemented by exercises which provide useful results in complex algebraic geometry.
Hodge Theory and Complex Algebraic Geometry I: Volume 1