Syllabus
1. Basic properties of projective space.
Definition of a projective space over R and C, linear objects, duality, corelation. 2. Classifications of quadrics in a projective space.
Definition of a quadric in projective space, inertia theorem, nullity space of a quadric, classification of quadrics especially for n = 2, 3. 3. Desargues, Pappos and Pascal theorem. 4.
Projective transformations and their real Jordan forms. Theorems on dimensions and on maximal linear subspaces on a quadric, polar properties, vertex of a quadric, general projective and affine classification of quadrics with application to n=2,3.
Tangent cone and base of a quadric.
Annotation
Projective extension of the affine space, projective space, homogeneous coordinates. Collineations.
Quadrics, their properties and classification.