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401-3146-12L 9 Credits BSC , MSC D-PHYS , D-MATH

Algebraic Geometry

Lecturers & Examiners: Dr. Johannes Schmitt
VVZ CR n/a

Last Updated: 2026-06-03 00:37:36

Abstract

This course is an Introduction to Algebraic Geometry (algebraic varieties and schemes).

Objective

Learning Algebraic Geometry.

Content

Affine Varieties The Zariski Topology The Sheaf of Regular Functions Morphisms Varieties Projective Varieties I: Topology Projective Varieties II: Ringed Spaces Grassmannians Birational Maps and Blowing Up Smooth Varieties The 27 Lines on a Smooth Cubic Surface Schemes Sheaves of Modules Quasi-coherent Sheaves Differentials Cohomology of Sheaves

Resources

Literature

Primary Reference: * Andreas Gathmann: Algebraic Geometry, https://agag-gathmann.math.rptu.de/class/alggeom-2021/alggeom-2021.pdf Secondary References: * Robin Hartshorne: Algebraic Geometry, Graduate Texts in Mathematics, Springer. * Miles Reid: Undergraduate Algebraic Geometry, Cambridge University Press. * Ravi Vakil: Foundations of Algebraic Geometry, http://math.stanford.edu/~vakil/216blog/ * David Eisenbud, Joe Harris: The Geometry of Schemes, Graduate Texts in Mathematics, Springer. * John Ottem, Geir Ellingsrud: Introduction to algebraic varieties, https://www.uio.no/studier/emner/matnat/math/MAT4210/data/mastermat4210.pdf * James Milne: Algebraic Geometry, http://www.jmilne.org/math/CourseNotes/AG.pdf * Qing Liu: Algebraic Geometry and Arithmetic Curves, Oxford Science Publications. * Ulrich Görtz and Torsten Wedhorn: Algebraic Geometry I, Advanced Lectures in Mathematics, Springer. * Igor Shafarevich: Basic Algebraic geometry 1 & 2, Springer-Verlag.

Learning Materials (Links)

General Information

Language
English
Levels
BSC , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
oral 30 minutes
The exam is offered only in the two examination sessions just after the course.

Course Components

Type Title Time & Place Hours
lecture Algebraic Geometry
This course is designed in a flipped classroom format. Monday 14-16 for presence and Q&A.
  • Mon 14:15-16:00 (HG G 5)
2 h weekly
exercise Algebraic Geometry
  • Tue 15:15-16:00 (HG D 7.1)
1 h weekly
revision course / private study Algebraic Geometry
Individual study without supervision.
No time listed 2 h weekly

Offered In