Automorphic Forms and the Picard Number of an Elliptic Surface (Aspects of Mathematics)

Language: English

Published by Vieweg+Teubner Verlag, E-402, 1984

3528085878 / 9783528085872

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Seller: Last Exit Books, Charlottesville, VA, U.S.A.Last Exit Books

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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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Title
Automorphic Forms and the Picard Number of an Elliptic Surface (Aspects of Mathematics)
Author
Peter F. Stiller
Publisher
Vieweg+Teubner Verlag, E-402
Publication year
1984
Condition
Very Good
Binding
Paperback
Language
English
ISBN 10
3528085878
ISBN 13
9783528085872

Last Exit Books

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