On the Geometry of Some Special Projective Varieties

By:

Francesco Russo

Format:

Paperback / softback

Series:

Lecture Notes of the Unione Matematica Italiana

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Description

Providing an introduction to both classical and modern techniques in projective algebraic geometry, this monograph treats the geometrical properties of varieties embedded in projective spaces, their secant and tangent lines, the behavior of tangent linear spaces, the algebro-geometric and topological obstructions to their embedding into smaller projective spaces, and the classification of extremal cases. It also provides a solution of Hartshorne’s Conjecture on Complete Intersections for the class of quadratic manifolds and new short proofs of previously known results, using the modern tools of Mori Theory and of rationally connected manifolds. The new approach to some of the problems considered can be resumed in the principle that, instead of studying a special embedded manifold uniruled by lines, one passes to analyze the original geometrical property on the manifold of lines passing through a general point and contained in the manifold. Once thisembedded manifold, usually of lower codimension, is classified, one tries to reconstruct the original manifold, following a principle appearing also in other areas of geometry such as projective differential geometry or complex geometry.

Release date Australia

February 1st, 2016

Author

Francesco Russo

Audience

Professional & Vocational

Edition

1st ed. 2016

Illustrations

XXVI, 232 p.

Pages

232

Series

Lecture Notes of the Unione Matematica Italiana

Dimensions

155x235x14

ISBN-13

9783319267647

Product ID

24148272

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