On the Geometry of Some Special Projective Varieties
| Autor: | Francesco Russo |
|---|---|
| EAN: | 9783319267654 |
| eBook Format: | |
| Sprache: | Englisch |
| Produktart: | eBook |
| Veröffentlichungsdatum: | 25.01.2016 |
| Kategorie: | |
| Schlagworte: | 14E05 14E30 14J70 14M07 14M10 14M22 14N05 Hartshorne Conjecture on Complete intersection Secant varieties hypersurfaces with v special uniruled and/or rationally connected manifolds varieties with (local) quadratic entry locus [ (L)QEL-manifold] |
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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.Verwandte Artikel
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