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Department of Mathematical Sciences, Unit Catalogue 2011/12


MA40188: Algebraic curves

Click here for further information Credits: 6
Click here for further information Level: Masters UG & PG (FHEQ level 7)
Click here for further information Period: Semester 2
Click here for further information Assessment: EX 100%
Click here for further information Supplementary Assessment: MA40188 Mandatory Extra Work (where allowed by programme regulations)
Click here for further information Requisites: Before taking this unit you must take MA30204
Click here for further information 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.
Click here for further informationProgramme availability:

MA40188 is Optional on the following programmes:

Department of Computer Science
  • USCM-AFB13 : BSc (hons) Computer Science with Mathematics (Full-time) - Year 3
  • USCM-AKB14 : BSc (hons) Computer Science with Mathematics (Full-time with Thick Sandwich Placement) - Year 4
  • USCM-AAB14 : BSc (hons) Computer Science with Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
Department of Mathematical Sciences
  • USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 3
  • USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 4
  • USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USMA-AFB13 : BSc (hons) Mathematics (Full-time) - Year 3
  • USMA-AKB14 : BSc (hons) Mathematics (Full-time with Thick Sandwich Placement) - Year 4
  • USMA-AFB01 : BSc (hons) Mathematics and Statistics (Full-time) - Year 3
  • USMA-AKB02 : BSc (hons) Mathematics and Statistics (Full-time with Thick Sandwich Placement) - Year 4
  • USMA-AAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USMA-AAB14 : BSc (hons) Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USMA-AFB05 : BSc (hons) Statistics (Full-time) - Year 3
  • USMA-AKB06 : BSc (hons) Statistics (Full-time with Thick Sandwich Placement) - Year 4
  • USMA-AAB06 : BSc (hons) Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USMA-AFM14 : MMath Mathematics (Full-time) - Year 3
  • USMA-AFM14 : MMath Mathematics (Full-time) - Year 4
  • USMA-AAM15 : MMath Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • TSMA-AFM09 : MSc Mathematical Sciences (Full-time) - Year 1
  • TSMA-APM09 : MSc Mathematical Sciences (Part-time) - Year 1
  • TSMA-APM09 : MSc Mathematical Sciences (Part-time) - Year 2
Department of Physics
  • USXX-AFM01 : MSci (hons) Mathematics and Physics (Full-time) - Year 4

NB. Programmes and units are subject to change at any time, in accordance with normal University procedures.