Inhalt des Dokuments
Algebraic Geometry 2
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.
549||Prof. Dr. Peter Bürgisser
There will be a lecture on Wednesday, December 9th, from 8:15 - 9:45 in MA-316.
prospective contents of this lecture will be the following:
(see also Shafarevich, Basic Algebraic Geometry, Volume I)
- Chapter 1. Local Properties
- Formal power series
- Repetition: local rings and tangent spaces
- Local parameters
- Power series expansion
- Local equations
- Chapter 2. Birational maps
- Blowup of projective spaces
- Local blowup
- Behaviour of subvarieties under blowup
- Chapter 3. Normal varieties
- Normal varieties
- Normalization of varieties
- Projective embedding of smooth varieties
- Chapter 4. Fibers of regular maps
- Nonsingularity of fibers