|
 Academic Year:
| 2012/3 |
| Owning Department/School:
| Department of Mathematical Sciences |
| Credits:
| 6 |
| Level:
| Masters UG & PG (FHEQ level 7) |
| Period: |
Semester 2 |
| Assessment:
| EX 100% |
| Supplementary Assessment: | MA40188 Mandatory Extra Work (where allowed by programme regulations) |
| Requisites:
| Before taking this unit you must take MA30204 |
| Description:
| NB. This unit is only available in academic years starting in an odd year. Aims: This is an advanced pure mathematics course providing an introduction to classical algebraic geometry via plane curves. It will show some of the links with other branches of mathematics. Learning Outcomes: At the end of the course students should be able to use homogeneous coordinates in projective space and to distinguish singular points of plane curves. They should be able to demonstrate an understanding of the difference between rational and nonrational curves, know examples of both, and be able to describe some special features of plane cubic curves. Content: To be chosen from: Affine and projective space. Polynomial rings and homogeneous polynomials. Ideals in the context of polynomial rings,the Nullstellensatz. Plane curves; degree; Bezout's theorem. Singular points of plane curves. Rational maps and morphisms; isomorphism and birationality. Curves of low degree (up to 3). Genus. Elliptic curves; the group law, nonrationality, the j invariant. Weierstrass p function. Quadric surfaces; curves of quadrics. Duals. |
| Programme availability: |
MA40188 is only available in academic years starting in an odd year. |