Algebraic Geometry (MAGIC074) |
GeneralThis course is part of the MAGIC core. Description
A first course in algebraic geometry, as the study of ringed spaces (of functions), which is a half-way house between classical algebraic geometry and modern scheme theory.
SemesterSpring 2016 (Monday, January 11 to Friday, March 18) Timetable
PrerequisitesSome familiarity with undergraduate commutative algebra (rings and their homomorphisms, ideals, quotient rings). It might be advisable to take MAGIC 073 (Commutative Algebra) in parallel. No prior knowledge of algebraic geometry is assumed.
SyllabusVarieties (affine, projective and ringed spaces) and their morphisms; Affine varieties as MaxSpec(A); Geometry via the Nullstellensatz; The Zariski topology; The Hilbert basis theorem and the Noetherian property; Irreducibility, dimension and tangent spaces; Affine and finite morphisms; Hypersurfaces; Projective spaces and the Segre embedding;
Students
Bibliography
Note: Clicking on the link for a book will take you to the relevant Google Book Search page. You may be able to preview the book there. On the right hand side you will see links to places where you can buy the book. There is also link marked 'Find this book in a library'. This sometimes works well, but not always. (You will need to enter your location, but it will be saved after you do that for the first time.) AssessmentThe assessment for this course will be via a single take-home paper in April with 2 weeks to complete and submit online. There will be a choice of 2 out of 3 questions, and a pass will be awarded if your script is judged to be correct on at least half of the material chosen.
MAGIC074 Algebraic Geometry Exam
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