On the Geometry of Some Special Projective Varieties

Nonfiction, Science & Nature, Mathematics, Geometry, Algebra
Cover of the book On the Geometry of Some Special Projective Varieties by Francesco Russo, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Francesco Russo ISBN: 9783319267654
Publisher: Springer International Publishing Publication: January 25, 2016
Imprint: Springer Language: English
Author: Francesco Russo
ISBN: 9783319267654
Publisher: Springer International Publishing
Publication: January 25, 2016
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Molecular Physiology and Ecophysiology of Sulfur by Francesco Russo
Cover of the book Homological Methods, Representation Theory, and Cluster Algebras by Francesco Russo
Cover of the book Multiresolution Approach to Processing Images for Different Applications by Francesco Russo
Cover of the book The Immune System in Space: Are we prepared? by Francesco Russo
Cover of the book Computer Aided Intervention and Diagnostics in Clinical and Medical Images by Francesco Russo
Cover of the book Flight of Mammals: From Terrestrial Limbs to Wings by Francesco Russo
Cover of the book Sustainable ICT, Education and Learning by Francesco Russo
Cover of the book Nailing the Written Emergency Medicine Board Examination by Francesco Russo
Cover of the book Supercomputing by Francesco Russo
Cover of the book Community-Based Disaster Risk Management in Azerbaijan by Francesco Russo
Cover of the book Mechanical Properties of Silicon Based Compounds: Silicides by Francesco Russo
Cover of the book The Washington State Census Board and Its Demographic Legacy by Francesco Russo
Cover of the book Cyber Security Cryptography and Machine Learning by Francesco Russo
Cover of the book Man-Machine Interactions 5 by Francesco Russo
Cover of the book Global Perspectives of Nanoscience and Engineering Education by Francesco Russo
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy