This advanced course is a continuation of the course in Algebraic Geometry from the summer term. The contents of said lecture are therefore prerequisite for attending. It will also be announced as a BMS advanced course.

The course will start on the 22nd of october.

Important information: There will be an Algebraic Geometry 3 lecture during the upcoming summer term. It will be possible to have one exam for both lectures.

Important information 2: There will be an additional lecture on wednesday december 9th. There will be no lecture on thursday december 17th.

Important information 3: You can now apply for an oral exam. Possible dates are february 17th (2pm-6pm) and 18th (8am-2pm). Please come to MA 319 or write an e-mail to breiding-at-math.tu-berlin.de, if you want an exam.

Important information 4: The next date for exams is april 19th (2pm-6pm). Please come to MA 319 or write an e-mail to breiding-at-math.tu-berlin.de, if you want an exam.

Students planning to write a Master's Thesis under supervision of Prof. Peter Bürgisser are expected to attend this lecture. 

There will be a lecture on Wednesday, December 9th, from 8:15 - 9:45 in MA-316.

The prospective contents of this lecture will be the following:
(see also Shafarevich, Basic Algebraic Geometry, Volume I)

• Chapter 1. Local Properties

1. Formal power series
2. Repetition: local rings and tangent spaces
3. Local parameters
4. Power series expansion
5. Local equations

• Chapter 2. Birational maps

1. Blowup of projective spaces
2. Local blowup
3. Behaviour of subvarieties under blowup

• Chapter 3. Normal varieties

1. Normal varieties
2. Normalization of varieties
3. Projective embedding of smooth varieties

• Chapter 4. Fibers of regular maps

1. Nonsingularity of fibers
2. Ramification
3. Irreducibility