Hodge Theory and Complex Algebraic Geometry I: Volume 1 by Claire Voisin,Leila Schneps

By Claire Voisin,Leila Schneps

the 1st of 2 volumes providing a contemporary advent to Kaehlerian geometry and Hodge constitution. The e-book begins with easy fabric on advanced variables, complicated manifolds, holomorphic vector bundles, sheaves and cohomology concept, the latter being taken care of in a extra theoretical means than is common in geometry. the writer then proves the Kaehler identities, which ends up in the difficult Lefschetz theorem and the Hodge index theorem. The publication culminates with the Hodge decomposition theorem. The meanings of those effects are investigated in numerous instructions. thoroughly self-contained, the booklet is perfect for college students, whereas its content material offers an account of Hodge idea and intricate algebraic geometry as has been built by means of P. Griffiths and his college, by means of P. Deligne, and via S. Bloch. The textual content is complemented by way of routines which offer necessary ends up in complicated algebraic geometry.

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