On the geometry of some special projective varieties /

On the geometry of some special projective varieties /

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Bibliographic Details
Author / Creator:	Russo, Francesco, 1959- author.
Imprint:	Cham : Springer, [2016]
Description:	1 online resource : illustrations
Language:	English
Series:	Lecture notes of the Unione Matematica Italiana ; 18 Lecture notes of the Unione Matematica Italiana ; 18.
Subject:	Geometry, Algebraic. Algebraic varieties. Algebraic varieties. Geometry, Algebraic. Electronic books.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11252206

Hidden Bibliographic Details
ISBN:	9783319267654 3319267655 3319267647 9783319267647 9783319267647
Digital file characteristics:	text file PDF
Notes:	"Winner of the UMI Book Prize, 2015"--Cover. Includes bibliographical references and index. English. Online resource; title from PDF title page (EBSCO, viewed February 01, 2016).
Summary:	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.
Other form:	Printed edition: 9783319267647
Standard no.:	10.1007/978-3-319-26765-4

Description
Summary:	<p>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.</p> 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.
Item Description:	"Winner of the UMI Book Prize, 2015"--Cover.
Physical Description:	1 online resource : illustrations
Bibliography:	Includes bibliographical references and index.
ISBN:	9783319267654 3319267655 3319267647 9783319267647