Trade pB. 8vo. Freidrich Vieweg & Sohn, Braunschweig, Germany. 1984. 194 pages. Aspects of Mathematics, Vol. 5. Wrappers lightly worn with some light shelf-wear to the extremities present. Book is free of ownership marks. Text is clean and free of marks. Binding tight and solid. In studying an algebraic surface E, which we assume is non-singular and projective over the field of complex numbers t, it is natural to study the curves on this surface. In order to do this one introduces various equivalence relations on the group of divisors (cycles of codimension one). One such relation is algebraic equivalence and we denote by NS(E) the group of divisors modulo algebraic equivalence which is called the N~ron-Severi group of the surface E. This is known to be a finitely generated abelian group which can be regarded naturally as a subgroup of 2 H (E, Z). The rank of NS(E) will be denoted p and is known as the Picard number of E. 2 Every divisor determines a cohomology class in H(E, E) which is of I type (1,1) , that is to say a class in H(E,9! ) which can be viewed as a 2 subspace of H(E, E) via the Hodge decomposition. The Hodge Conjecture asserts in general that every rational cohomology class of type (p, p) is algebraic. In our case this is the Lefschetz Theorem on (I, l) -classes: Every cohomology class 2 2 is the class associated to some divisor. Here we are writing H (E, Z) for 2 its image under the natural mapping into H (E, t). Thus NS(E) modulo 2 torsion is Hl(E, n! ) n H(E, Z) and th 1 b I f h -~ p measures e a ge ra c part 0 t e cohomology. ; 8vo 8" - 9" tall.

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Bibliographic Details

Title: Automorphic Forms and the Picard Number of an Elliptic Surface (Aspects of Mathematics)
Publisher: Vieweg+Teubner Verlag, E-328
Publication Date: 1984
Language: English
ISBN 10: 3528085878
ISBN 13: 9783528085872
Binding: Paperback
Condition: Very Good

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In studying an algebraic surface E, which we assume is non-singular and projective over the field of complex numbers t, it is natural to study the curves on this surface. In order to do this one introduces various equivalence relations on the group of divisors (cycles of codimension one). One such relation is algebraic equivalence and we denote by NS(E) the group of divisors modulo algebraic equivalence which is called the N~ron-Severi group of the surface E. This is known to be a finitely generated abelian group which can be regarded naturally as a subgroup of 2 H (E,Z). The rank of NS(E) will be denoted p and is known as the Picard number of E. 2 Every divisor determines a cohomology class in H(E,E) which is of I type (1,1), that is to say a class in H(E,9!) which can be viewed as a 2 subspace of H(E,E) via the Hodge decomposition. The Hodge Conjecture asserts in general that every rational cohomology class of type (p,p) is algebraic. In our case this is the Lefschetz Theorem on (I,l)-classes: Every cohomology class 2 2 is the class associated to some divisor. Here we are writing H (E,Z) for 2 its image under the natural mapping into H (E,t). Thus NS(E) modulo 2 torsion is Hl(E,n!) n H(E,Z) and th 1 b i f h -~ p measures e a ge ra c part 0 t e cohomology.

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