
65411/412: 
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.

Literature: 
Atiyah, Macdonald: Introduction to Commutative Algebra, AddisonWesley 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


Exercises: 


