Hodge Theory and Complex Algebraic Geometry I: Volume 1 - Claire Voisin & Leila Schneps

Hodge Theory and Complex Algebraic Geometry I: Volume 1

By Claire Voisin & Leila Schneps

  • Release Date: 2002-12-05
  • Genre: Mathematics
Hodge Theory and Complex Algebraic Geometry I: Volume 1 book review score

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Hodge Theory and Complex Algebraic Geometry I: Volume 1 Claire Voisin & Leila Schneps Book Review Score: ★★★★★ 5/5 stars

The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure. The book starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory, the latter being treated in a more theoretical way than is usual in geometry. The author then proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The book culminates with the Hodge decomposition theorem. The meanings of these results are investigated in several directions. Completely self-contained, the book is ideal for students, while its content gives an account of Hodge theory and complex algebraic geometry as has been developed by P. Griffiths and his school, by P. Deligne, and by S. Bloch. The text is complemented by exercises which provide useful results in complex algebraic geometry.

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