Lecturer

Dr. Massimiliano Alessandro
Office hours: by appointment via email.

Time and Place

Lectures: Tuesday 16-18 in SR6, Wednesday 14-16 in SR6.
Exercise Class: Thursday 14-16 in SR6.

Note: The course will be held in English.

Content

• Hilbert's Basis theorem, Hilbert's Nullstellensatz
• modules, tensor products of modules
• localisation and local properties of rings and modules
• integral dependence, valuations, going-up and going-down theorems
• graded rings and modules
• affine varieties, projective varieties, Zariski topology
• morphisms and rational maps between varieties
• birational morphisms and blowups
• nonsingularity and smoothness

Prerequisites: Linear Algebra I and II, Algebra (recommended)

Registration

Please enroll in the course via the CMS website.

Exam Dates

First Exam: TBA
Second Exam: TBA

Important: If you are unable to register for the first or second exam in LSF, please contact me by email (your examination office must send me a confirmation in good time before the exam stating that you are permitted to take it). If permitted by your examination regulations, the second exam may be used to improve your grade.

Exam criteria

Exercise sheets are uploaded weekly on the CMS website and are to be solved by the following week (Tuesday). The submission of the exercise sheets takes place via CMS. The sheets are corrected during the exercise class and returned with points awarded.

In order to obtain a grade, the following criteria are to be fulfilled:

• regular participation at the exercise classes,


• at least 50% of the points from the exercise sheets attained,


• the passed exam.

Literature

• Atiyah, Macdonald. "Introduction to Commutative Algebra".


• Matsumura. Commutative Algebra.


• Matsumura. Commutative Ring Theory.


• Eisenbud. Commutative Algebra with a View Toward Algebraic Geometry.


• Hartshorne. Algebraic Geometry.


• Vakil. Foundations of Algebraic Geometry.


• Fulton. Algebraic Curves. An Introduction to Algebraic Geometry.


• Görtz, Wedhorn. Algebraic Geometry I