Schriftzug: Fachbereich Mathematik 
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Ingo Runkel

Algebraic Geometry - summer term 2018

Announcements:
  • [25.6] Tomorrow, Tuesday 26.6, there is no exercise class and no lecture. The exercise class will instead take place on Thu. 28.6, 8:30-10:00 in H5. This is also when the homework exercises 11 will be collected. Exercise sheet 12 will be posted tomorrow. The week after, exercise class and lecture on Tuesday will take place as usual (this still needs to be corrected in STiNE, it currently claims there is no lecture, but this is not true), and there will be a replacement lecture on Thu 5.7 8:30-10:00, also in H5.
Exercise sheets:
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
The exercises will be collected each Tuesday at the start of the exercise class.

Solutions:
Sketches of the solutions will be uploaded to the STiNE page of the exercise class.

When and where:
Lecture Tuesdays 12:15-13:45 in H3 and Thursdays 12:15-13:45 in H4. Exercise class Tuesdays 10:15-11:45 in 142.

Admission to the exam:
To be admitted to the exam you need to obtain at least half of the points available on the exercise sheets and you need to participate actively in the exercise class. There will be 12 exercise sheets with 24 points each.

Description:
This lecture provides an introduction to algebraic geometry with a focus on the relation between algebraic and geometric notions. A central point is the study of varieties over an algebraically closed field, described by solutions to polynomial equations. Topics will include: concepts from commutative algebra (Hilbert's Nullstellensatz, localisation, Krull-dimension), affine varieties, projective varieties, resulution of singularities, regular and singular points, algebraic curves.

Literature:
Here a list of possible books which will likely grow as the course proceeds.
  • Hartshorne, Algebraic Geometry (Springer) - only chapter I.
  • Hulek, Elementare Algebraische Geometrie (Vieweg+Teubner - in German)

 
  Seitenanfang  Impressum 2018-06-26, Ingo Runkel