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Hodge theory and complex algebraic g...

Voisin, Claire, (1962-)

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Hodge theory and complex algebraic geometry.. 2

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Hodge theory and complex algebraic geometry./ Claire Voisin ; translated by Leila Schneps.
作者:	Voisin, Claire,
其他作者:	Schneps, Leila.
出版者:	Cambridge :Cambridge University Press, : 2003.,
面頁冊數:	ix, 351 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Hodge theory. -
電子資源:	https://doi.org/10.1017/CBO9780511615177
ISBN:	9780511615177

Hodge theory and complex algebraic geometry.. 2
Voisin, Claire,1962-

Hodge theory and complex algebraic geometry.2[electronic resource] /Claire Voisin ; translated by Leila Schneps. - Cambridge :Cambridge University Press,2003. - ix, 351 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;77. - Cambridge studies in advanced mathematics ;77..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

The 2003 second volume of this account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. Proofs of the Lefschetz theorem on hyperplane sections, the Picard-Lefschetz study of Lefschetz pencils, and Deligne theorems on the degeneration of the Leray spectral sequence and the global invariant cycles follow. 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 of the book is devoted to the relationships between Hodge theory and algebraic cycles. The book concludes with the example of cycles on abelian varieties, where some results of Bloch and Beauville, for example, are expounded. The text is complemented by exercises giving useful results in complex algebraic geometry. It will be welcomed by researchers in both algebraic and differential geometry.

ISBN: 9780511615177Subjects--Topical Terms:

701563
Hodge theory.

LC Class. No.: QA564 / .V6513 2003

Dewey Class. No.: 516.35

Hodge theory and complex algebraic geometry.. 2
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240 1 0 $a Theorie de Hodge et geometrie algebrique complexe. $l English
245 1 0 $a Hodge theory and complex algebraic geometry. $n 2 $h [electronic resource] / $c Claire Voisin ; translated by Leila Schneps.
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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
520 $a The 2003 second volume of this account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. Proofs of the Lefschetz theorem on hyperplane sections, the Picard-Lefschetz study of Lefschetz pencils, and Deligne theorems on the degeneration of the Leray spectral sequence and the global invariant cycles follow. 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 of the book is devoted to the relationships between Hodge theory and algebraic cycles. The book concludes with the example of cycles on abelian varieties, where some results of Bloch and Beauville, for example, are expounded. The text is complemented by exercises giving useful results in complex algebraic geometry. It will be welcomed by researchers in both algebraic and differential geometry.
650 0 $a Hodge theory. $3 701563
650 0 $a Geometry, Algebraic. $3 532048
700 1 $a Schneps, Leila. $3 745251
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