Get Hodge Theory and Complex Algebraic Geometry I: Volume 1 PDF

By Claire Voisin,Leila Schneps

the 1st of 2 volumes providing a latest advent to Kaehlerian geometry and Hodge constitution. The ebook begins with easy fabric on advanced variables, advanced manifolds, holomorphic vector bundles, sheaves and cohomology idea, the latter being handled in a extra theoretical method than is common in geometry. the writer then proves the Kaehler identities, which results in the tough Lefschetz theorem and the Hodge index theorem. The e-book 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 offers an account of Hodge idea and intricate algebraic geometry as has been built by way of P. Griffiths and his tuition, by way of P. Deligne, and by way of S. Bloch. The textual content is complemented through routines which supply important leads to complicated algebraic geometry.

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