Hodge Theory and Complex Algebraic Geometry I

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Mathematics - Algebra
Hodge Theory and Complex Algebraic...

Hodge Theory and Complex Algebraic Geometry I

Name: Hodge Theory and Complex Algebraic Geometry I
ISBN: 9780521802604

Claire Voisin, Leila Schneps (Translator)

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Main subject categories: • Hodge theory • Algebraic geometry • Holomorphic functions • Complex manifolds • Kähler metrics • Sheaves and cohomology • Kähler manifolds • Holomorphic de Rham complexes • Spectral sequences • Hodge theory • Cycles and cycle classes • Deligne–Beilinson Cohomology and the Abel–Jacobi Map

This is a modern introduction to Kählerian geometry and Hodge structure. Coverage begins with variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory (with the latter being treated in a more theoretical way than is usual in geometry). The book culminates with the Hodge decomposition theorem. In between, the author proves the Kähler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The second part of the book investigates the meaning of these results in several directions.

الفئات:

Mathematics - Algebra

المجلد:

عام:

2002

الإصدار:

الناشر:

Cambridge University Press [CUP]

اللغة:

english

الصفحات:

335