Algebraic Geometry (MAGIC074)
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This course is part of the MAGIC core.
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.
Autumn 2019 (Monday, October 7 to Friday, December 13)
Some 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.
Varieties (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;
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