Bernd Siebert
Schriftzug: Fachbereich Mathematik 
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65-411/412: Lecture Course: Topics in Algebraic Geometry
Lecturer: Bernd Siebert
Description: In the first half of the class we will complete the study of abstract algebraic geometry following Hartshorne's classic "Algebraic geometry", notably introducing cohommological methods. In the second half we will apply the theory to the study of two famous moduli problems. The first concerns the parametrization of closed subschemes of projective space, leading to the Hilbert scheme. The second concerns moduli spaces of closed curves. We find that a satisfying treatment leads to the concept of an algebraic stack, a generalization of the notion of scheme taking track of automorphisms of the parametrized objects.
Participants are urged to also attend the seminar on complex surfaces and threefolds, which will complement nicely the introduction to algebraic geometry by more concrete examples.
Recitations will be integrated into class on Fridays.
Prerequisites: Knowledge of basic concepts in algebraic varieties and scheme theory as taught in Algebraic Geometry I and II.
Exam: Oral examination.
Atiyah, Macdonald: Introduction to Commutative Algebra, Addison-Wesley 1969
Hartshorne: Algebraic Geometry, Springer 1977
Arbarello, Cornalba, Griffiths: Geometry of Algebraic Curves, Springer 1977
Time and venue:
Lectures: TUE 14:15–15:345 Geom H1, FRI 12:00–13:30 Geom H3

  Seitenanfang  Impressum 2016-03-16, Bernd Siebert