Geometry of Quadratic Equations
This Module is offered by TUM Department of Mathematics.
This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective
MA5221 is a semester module
in English language
at Master’s level
which is offered once.
This module description is valid from SS 2016 to WS 2016/7.
|Total workload||Contact hours||Credits (ECTS)|
Linear systems of quadrics,
base loci, discriminant loci,
Jacobian and Reye varieties,
complete intersections of quadrics,
examples from classical algebraic geometry,
symmetric determinantal representations of hypersurfaces,
conic fibrations and rationality questions
At the end of the lecture, the students are familiar with the theory of linear systems of quadrics and their attributes, such as base loci and discriminant loci. They will know the basic examples from classical algebraic geometry, and will be able to perform simple computations with them. The will understand the connection to complete intersection and other classical constructions. Moreover, they will be able to apply the theory to the symmetric determinantal representations of hypersurfaces. Finally, they will be able to understand the connection to conic fibrations and rationality questions.
MA1101 Linear Algebra 1
MA1102 Linear Algebra 2
useful, but not necessary:
MA5120 Algebra 2
MA5107 Algebraic Geometry
MA3203 Projective Geometry
Learning and Teaching Methods
The module consists of a series of lectures. In the lectures, theoretical principles and examples are presented.
Dolgachev: Classical Algebraic Geometry
Description of exams and course work
The examination will be oral (30 minutes). Students are supposed to know the basic objects and notions of the lecture, as well as the main theorems connected these. They are supposed to know the basic examples of linear systems of quadrics from classical algebraic geometry. They are supposed to perform elementary computations, as well as to solve simple exercises with them, such as computing the basic attributes of linear systems, e.g., base and discriminant loci. They are able to name and explain applications of the theorems to to algebraic surfaces, hypersurfaces, and rationality questions.
The exam may be repeated at the end of the semester.