On the Geometry of Some Special Projective Varieties

On the Geometry of Some Special Projective Varieties
Author :
Publisher : Springer
Total Pages : 257
Release :
ISBN-10 : 9783319267654
ISBN-13 : 3319267655
Rating : 4/5 (54 Downloads)

Book Synopsis On the Geometry of Some Special Projective Varieties by : Francesco Russo

Download or read book On the Geometry of Some Special Projective Varieties written by Francesco Russo and published by Springer. This book was released on 2016-01-25 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


On the Geometry of Some Special Projective Varieties Related Books

On the Geometry of Some Special Projective Varieties
Language: en
Pages: 257
Authors: Francesco Russo
Categories: Mathematics
Type: BOOK - Published: 2016-01-25 - Publisher: Springer

DOWNLOAD EBOOK

Providing an introduction to both classical and modern techniques in projective algebraic geometry, this monograph treats the geometrical properties of varietie
The Geometry of some special Arithmetic Quotients
Language: en
Pages: 347
Authors: Bruce Hunt
Categories: Mathematics
Type: BOOK - Published: 2006-11-14 - Publisher: Springer

DOWNLOAD EBOOK

The book discusses a series of higher-dimensional moduli spaces, of abelian varieties, cubic and K3 surfaces, which have embeddings in projective spaces as very
Lectures on Curves, Surfaces and Projective Varieties
Language: en
Pages: 512
Authors: Mauro Beltrametti
Categories: Mathematics
Type: BOOK - Published: 2009 - Publisher: European Mathematical Society

DOWNLOAD EBOOK

This book offers a wide-ranging introduction to algebraic geometry along classical lines. It consists of lectures on topics in classical algebraic geometry, inc
Algebraic Geometry I
Language: en
Pages: 208
Authors: David Mumford
Categories: Mathematics
Type: BOOK - Published: 1976 - Publisher: Springer

DOWNLOAD EBOOK

From the reviews: "Although several textbooks on modern algebraic geometry have been published in the meantime, Mumford's "Volume I" is, together with its prede
Automorphisms in Birational and Affine Geometry
Language: en
Pages: 509
Authors: Ivan Cheltsov
Categories: Mathematics
Type: BOOK - Published: 2014-06-11 - Publisher: Springer

DOWNLOAD EBOOK

The main focus of this volume is on the problem of describing the automorphism groups of affine and projective varieties, a classical subject in algebraic geome