Syllabus
Algebraic geometry in affine spaces
- Galois correspondence IV, Hilbert's Nullstellensatz
- irreducible decomposition
- coordinate rings, local properties of curves
Algebraic geometry in projective spaces
- projective specas, homogeneous polynomials and ideals
- projective irreducibility, projective Nullstellensatz
- relation of affine and projective curves
- Bezout's theorem
- elliptic curves.
Annotation
A recommended course for Information Security and specialization Mathematical Structures within General
Mathematics. This is an introductory lecture to basic algebraic geometry focused on curves. The course is concerned with the basic notions (affine and projective variety, mappings on varieties, coordinate rings), local properties of curves, Bezout theorem and elliptic curves.