The 1st of 2 volumes delivering a contemporary creation to Kaehlerian geometry and Hodge constitution. The booklet starts off with uncomplicated fabric on advanced variables, advanced manifolds, holomorphic vector bundles, sheaves and cohomology idea, the latter being taken care of in a extra theoretical method than is common in geometry. the writer then proves the Kaehler identities, which ends up in the demanding Lefschetz theorem and the Hodge index theorem. The booklet culminates with the Hodge decomposition theorem. The meanings of those effects are investigated in different instructions. thoroughly self-contained, the e-book is perfect for college kids, whereas its content material supplies an account of Hodge thought and intricate algebraic geometry as has been constructed by way of P. Griffiths and his tuition, through P. Deligne, and via S. Bloch. The textual content is complemented via routines which supply priceless leads to advanced algebraic geometry.
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