The second volume of this modern account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. The main results are the generalized Noether-Lefschetz theorems, the generic triviality of the Abel-Jacobi maps, and most importantly, Nori's connectivity theorem, which generalizes the above. The last part deals with the relationships between Hodge theory and algebraic cycles. The text is complemented by exercises offering useful results in complex algebraic geometry. Also available: Volume I 0-521-80260-1 Hardback $60.00 C
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"Mathematical rewards [await] those who invest their mathematical energies in this beautiful pair of volumes." Bulletin of the AMS
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The second volume of this modern and unique account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. The main results of the second part are the generalized Noether-Lefschetz theorems, the generic triviality of the Abel-Jacobi maps, and most importantly Nori's connectivity theorem, which generalizes the above.The last part deals with the relationships between Hodge theory and algebraic cycles. The text is complemented by exercises giving useful results in complex algebraic geometry. It will be welcomed by researchers in algebraic and differential geometry.
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First Sentence:
This chapter is devoted to a presentation of Morse theory on affine varieties, and its application to the proof of the famous Lefschetz theorem on hyperplane sections, which is the following statement. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
ample hypersurfaces, invariant cycles theorem, cycle class map, vanishing spheres, universal hypersurface, infinitesimal invariant, restriction arrow, monodromy action, closed algebraic subset, composed functor, proper analytic subsets, meromorphic form, smooth hyperplane section, algebraic cycles, connectivity theorem, vanishing cohomology, local lifting, rational equivalence, vanishing cycles, ordinary double point, spectral sequence, hyperplane sections, projective bundle, smooth projective surface, monodromy representation Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Abel Jacobi, Proof Note, The Lefschet New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This chapter is devoted to a presentation of Morse theory on affine varieties, and its application to the proof of the famous Lefschetz theorem on hyperplane sections, which is the following statement. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
ample hypersurfaces, invariant cycles theorem, cycle class map, vanishing spheres, universal hypersurface, infinitesimal invariant, restriction arrow, monodromy action, closed algebraic subset, composed functor, proper analytic subsets, meromorphic form, smooth hyperplane section, algebraic cycles, connectivity theorem, vanishing cohomology, local lifting, rational equivalence, vanishing cycles, ordinary double point, spectral sequence, hyperplane sections, projective bundle, smooth projective surface, monodromy representation Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Abel Jacobi, Proof Note, The Lefschet New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 11
books:
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- New Trends in Algebraic Geometry (London Mathematical Society Lecture Note Series) by K. Hulek on page 342, and Back Matter
- Lectures on Vanishing Theorems (Oberwolfach Seminars) by Esnault in Back Matter
- Geometry of Algebraic Curves: Volume I (Grundlehren der mathematischen Wissenschaften) by Enrico Arbarello on page 342
- Real and Complex Analysis (International Series in Pure and Applied Mathematics) by Walter Rudin in Back Matter
- Topics in Transcendental Algebraic Geometry. (AM-106) (Annals of Mathematics Studies) by Phillip A. Griffiths in Back Matter
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