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Fachgebiet Algorithmische AlgebraAlgebraic Geometry 2

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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.

Attention

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

Lecture times

Lecture times
Thursday
10:15-11:45
MA 549
Prof. Dr. Peter Bürgisser

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

Contents

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

    Exams

    Exams
    Tuesday, April 19th
    Name
    2 - 2:30 pm
    M. Eisenhardt
    3 - 4 pm
    M. Malik
    5:30 pm - 6 pm
    M. Granz

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