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On the Geometry of Some Special Projective Varieties (Paperback, 1st ed. 2016)
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On the Geometry of Some Special Projective Varieties (Paperback, 1st ed. 2016)
Series: Lecture Notes of the Unione Matematica Italiana, 18
Expected to ship within 10 - 15 working days
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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 this
embedded 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.
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