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)

Label
On the Geometry of Some Special Projective Varieties
Title
On the Geometry of Some Special Projective Varieties
Statement of responsibility
by Francesco Russo
Creator
Contributor
Author
Provider
Subject
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 algebro-geometric 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
Member of
http://library.link/vocab/creatorName
Russo, Francesco
Image bit depth
0
LC call number
QA564-609
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)
Instantiates
Publication
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.Fulton-Hansen 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 n-covered 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
10.1007/978-3-319-26765-4
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-26765-4
Label
On the Geometry of Some Special Projective Varieties, by Francesco Russo, (electronic resource)
Publication
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.Fulton-Hansen 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 n-covered 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
10.1007/978-3-319-26765-4
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-26765-4

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