On the Geometry of Some Special Projective Varieties

• Main Author: Russo, Francesco (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Edition: 1st ed. 2016.
• Series: Lecture Notes of the Unione Matematica Italiana, 18
• Subjects: Mathematics.; Algebraic geometry.; Commutative algebra.; Commutative rings.; Geometry.; Algebraic Geometry.; Commutative Rings and Algebras.

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 topologica...

Table of 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.