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The Resource On the Geometry of Some Special Projective Varieties, by Francesco Russo, (electronic resource)
On the Geometry of Some Special Projective Varieties, by Francesco Russo, (electronic resource)
Resource Information
The item On the Geometry of Some Special Projective Varieties, by Francesco Russo, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item On the Geometry of Some Special Projective Varieties, by Francesco Russo, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 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 algebrogeometric and topological obstructions to their embedding into smaller projective spaces, and the classification of extremal cases. It also provides a solution of Hartshorneâs 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
 Language
 eng
 Edition
 1st ed. 2016.
 Extent
 XXVI, 232 p.
 Contents

 Preface.Introduction
 1.Tangent cones, tangent spaces, tangent stars; secant, tangent and tangent star varieties to an algebraic variety
 2.Basics of Deformation Theory of Rational Curves on Projective Varieties
 3.FultonHansen Connectedness Theorem, Scorza Lemma and their applications to projective geometry
 4.Local quadratic entry locus manifolds and conic connected manifolds
 5.Hartshorne Conjectures and Severi varieties
 6.Varieties ncovered by curves of a fixed degree and the XJC
 7. Hypersurfaces with vanishing hessian.Bibliography
 Isbn
 9783319267654
 Label
 On the Geometry of Some Special Projective Varieties
 Title
 On the Geometry of Some Special Projective Varieties
 Statement of responsibility
 by Francesco Russo
 Language
 eng
 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 algebrogeometric and topological obstructions to their embedding into smaller projective spaces, and the classification of extremal cases. It also provides a solution of Hartshorneâs 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
 http://library.link/vocab/creatorName
 Russo, Francesco
 Image bit depth
 0
 LC call number
 QA564609
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName
 SpringerLink
 Series statement
 Lecture Notes of the Unione Matematica Italiana,
 Series volume
 18
 http://library.link/vocab/subjectName

 Mathematics
 Algebraic geometry
 Commutative algebra
 Commutative rings
 Geometry
 Mathematics
 Algebraic Geometry
 Commutative Rings and Algebras
 Geometry
 Label
 On the Geometry of Some Special Projective Varieties, by Francesco Russo, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Preface.Introduction  1.Tangent cones, tangent spaces, tangent stars; secant, tangent and tangent star varieties to an algebraic variety  2.Basics of Deformation Theory of Rational Curves on Projective Varieties  3.FultonHansen Connectedness Theorem, Scorza Lemma and their applications to projective geometry  4.Local quadratic entry locus manifolds and conic connected manifolds  5.Hartshorne Conjectures and Severi varieties  6.Varieties ncovered by curves of a fixed degree and the XJC  7. Hypersurfaces with vanishing hessian.Bibliography
 Dimensions
 unknown
 Edition
 1st ed. 2016.
 Extent
 XXVI, 232 p.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319267654
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783319267654
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319267654
 Label
 On the Geometry of Some Special Projective Varieties, by Francesco Russo, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Preface.Introduction  1.Tangent cones, tangent spaces, tangent stars; secant, tangent and tangent star varieties to an algebraic variety  2.Basics of Deformation Theory of Rational Curves on Projective Varieties  3.FultonHansen Connectedness Theorem, Scorza Lemma and their applications to projective geometry  4.Local quadratic entry locus manifolds and conic connected manifolds  5.Hartshorne Conjectures and Severi varieties  6.Varieties ncovered by curves of a fixed degree and the XJC  7. Hypersurfaces with vanishing hessian.Bibliography
 Dimensions
 unknown
 Edition
 1st ed. 2016.
 Extent
 XXVI, 232 p.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319267654
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783319267654
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319267654
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.bu.edu/portal/OntheGeometryofSomeSpecialProjective/D5FpWKmdOdY/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.bu.edu/portal/OntheGeometryofSomeSpecialProjective/D5FpWKmdOdY/">On the Geometry of Some Special Projective Varieties, by Francesco Russo, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.bu.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.bu.edu/">Boston University Libraries</a></span></span></span></span></div>