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Algebraic Geometry

By Edward H. Spanier

ISBN-10: 0070598835

ISBN-13: 9780070598836

Meant to be used either as a textual content and a reference, this e-book is an exposition of the basic principles of algebraic topology. the 1st 3rd of the ebook covers the elemental workforce, its definition and its program within the examine of masking areas. the point of interest then turns to homology thought, together with cohomology, cup items, cohomology operations, and topological manifolds. the rest 3rd of the e-book is dedicated to Homotropy concept, masking uncomplicated proof approximately homotropy teams, purposes to obstruction conception, and computations of homotropy teams of spheres. within the later elements, the most emphasis is at the software to geometry of the algebraic instruments constructed previous.

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Extra resources for Algebraic topology

Sample text

Taking A = X, we obtain CPx == 4~, which is the functional counterpart of PANNELLI'S second relation, W = 4 Q o + 1. Thus, in the present theory, PANNELLI'S equations appear as numerical aspects of equivalence relations which are themselves merely special cases of general functional results; we shall see shortly that SEVERI'S equation is capable of a similar interpretation. Writing the above equivalence in the form CPA == (A3) + 2 (A2X) + (AX2), we observe that it enables us to define the canonical series ICPAI in all cases, even when A is reducible or virtual.

More precisely, in the case d = 3, if there is a congruence of curves, its irregularity is at least q - Pg (;;; 3), while if there is a pencil of surfaces, its genus is at least q - Pg - 1 (;;; 2). COMESSATTI'S demonstration, like CASTELNUOVO'S, is transcendental, but, as D'ORGEVAL [1J has observed in the case d = 2, a geometrical proof may be given. Following CASTELNUOVO, we consider on ~ a continuous system {C} of hypersurfaces consisting of ooq disequivalent linear systems: such systems can always be found on Va.

Moreover, it depends only on

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