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Year: 1978 Publisher: Delft Waltman
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ISBN: 9783540705192 Year: 2008 Publisher: Berlin, Heidelberg Springer-Verlag Berlin Heidelberg
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This volume presents the construction of canonical modular compactifications of moduli spaces for polarized Abelian varieties (possibly with level structure), building on the earlier work of Alexeev, Nakamura, and Namikawa. This provides a different approach to compactifying these spaces than the more classical approach using toroical embeddings, which are not canonical. There are two main new contributions in this monograph: (1) The introduction of logarithmic geometry as understood by Fontaine, Illusie, and Kato to the study of degenerating Abelian varieties; and (2) the construction of canonical compactifications for moduli spaces with higher degree polarizations based on stack-theoretic techniques and a study of the theta group.
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ISBN: 9783034800150 Year: 2011 Publisher: Basel Springer Basel
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The goal of the book is to present, in a complete and comprehensive way, areas of current research interlacing around the Poncelet porism: dynamics of integrable billiards, algebraic geometry of hyperelliptic Jacobians, and classical projective geometry of pencils of quadrics. The most important results and ideas, classical as well as modern, connected to the Poncelet theorem are presented, together with a historical overview analyzing the classical ideas and their natural generalizations. Special attention is paid to the realization of the Griffiths and Harris programme about Poncelet-type problems and addition theorems. This programme, formulated three decades ago, is aimed to understanding the higher-dimensional analogues of Poncelet problems and the realization of the synthetic approach of higher genus addition theorems.
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ISBN: 9783642108891 Year: 2011 Publisher: Berlin, Heidelberg Springer Berlin Heidelberg
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B.L. van der Waerden: Démonstration algébrique du théorème de Riemann-Roch.- F. Severi: Del teorema di Riemann-Roch per curve, superficie e varietà. Le origini storiche e lo stato attuale.- F. Hirzebruch: Arithmetic genera and the theorem of Riemann-Roch.
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ISBN: 9783642109522 Year: 2011 Publisher: Berlin, Heidelberg Springer Berlin Heidelberg
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G. De Rham: La théorie des formes différentiielles extérieures et l´homologie des variétés différentiablles.- G. Fichera: Teoria assiomatica delle forme armoniche.- W.V.D. Hodge: Differential forms in algebraic geometry.- D.B. Scott: Correspondences between algebraic surfaces.- P.Dolbeault: Sur le groupe de cohomologie entière de dimension d´une variété analytique complexe.- E. Kähler: Der innere Differentialkalkül.
Book
ISBN: 9783642110870 Year: 2011 Publisher: Berlin, Heidelberg Springer Berlin Heidelberg
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Lectures: A. Beauville: Surfaces algébriques complexes.- F.A. Bogomolov: The theory of invariants and its applications to some problems in the algebraic geometry.- E. Bombieri: Methods of algebraic geometry in Char. P and their applications.- Seminars: F. Catanese: Pluricanonical mappings of surfaces with K² =1,2, q=pg=0.- F. Catanese: On a class of surfaces of general type.- I. Dolgacev: Algebraic surfaces with p=pg =0.- A. Tognoli: Some remarks about the "Nullstellensatz".
Book
ISBN: 9783540337089 Year: 2008 Publisher: Berlin, Heidelberg Springer-Verlag Berlin Heidelberg
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Issu d'un cours de maîtrise de l'Université Paris VII, ce texte est réédité tel qu'il était paru en 1978. A propos du théorème de Bézout sont introduits divers outils nécessaires au développement de la notion de multiplicité d'intersection de deux courbes algébriques dans le plan projectif complexe. Partant des notions élémentaires sur les sous-ensembles algébriques affines et projectifs, on définit les multiplicités d'intersection et interprète leur somme entermes du résultant de deux polynômes. L'étude locale est prétexte à l'introduction des anneaux de série formelles ou convergentes ; elle culmine dans le théorème de Puiseux dont la convergence est ramenée par des éclatements à celle du théorème des fonctions implicites. Diverses figures éclairent le texte: on y "voit" en particulier que l'équation homogène x3+y3+z3 = 0 définit un tore dans le plan projectif complexe.
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