M.Sc.-Math. Roberto Laface

LecturesTuesdays 14:00 - 16:00 (A410) Thurdays 14:00 - 16:00 (G117) Exercise SessionsFridays14:00 - 16:00 (G123) | Aim of the courseThe aim of this class is to continue the study of
schemes started in the course "Algebraic Geometry I", in order to get
to the geometry underlying the abstract machinery introducted by Alexander Grothendieck. SyllabusAfter
introducing the concept of projective scheme, which turns out to be the
right setup for doing some true geometry, we will focus on applications
of scheme theory to the geometry of varieties. Among the topics we will
be dealing with, we have: - Bezout´s theorem
- Divisors
- Elliptic curves
- Coherent and quasi-coherent sheaves
- Vector bundles
- Differentials
- Cohomology of sheaves
- Riemann-Roch theorem for curves
- Riemann-Hurwitz formula
- Intersection theory
An exercise sheet will be uploaded here and on Stud.IP approximately one week before the class, whereas solutions to the problems will be made available shortly after the class. Also, some notes containing additional material will be made available, if necessary. - Exercise sheet 1
- Exercise sheet 2
- Exercise sheet 3
- Exercise sheet 4
- Exercise sheet 5
- Exercise sheet 6
- Exercise sheet 7
- Exercise sheet 8
- Exercise sheet 9
- Homework
- How to draw real algebraic curves for dummies
- Notes on Grassmannians on schemes
- Notes on module-like constructions for sheaves
Algebraic Geometry involves ideas from both the worlds of Algebra and Geometry; thus, in order to understand it properly, one must have a good knowledge of both commutative algebra and elementary algebraic geometry. As for commutative algebra, I strongly recommend As for geometry, Hartshorne's |