Algebraic Geometry Spring 2018

Lecturer
Prof. Emmanuel Kowalski
Lectures
Tue 15-17, HG F 26.3
Fri 08-10, HG F 26.3
Coordinator
Paul Steinmann
Exercise classes
Mo 12-13, HG F 26.3

Content

This course is an introduction to Algebraic Geometry (algebraic varieties and schemes). It is required to have a basic knowledge of Commutative Algebra.

Short Outline

  1. Classical Varieties
  2. Basic Theory of Schemes
  3. Curves

Exercises

We prepare an exercise sheet every two weeks. The new exercises will be posted here every other Friday. We expect you to look at the problems and to prepare questions for the exercise class one week after.

Please hand in your solutions in the exercise class or in your assistant's box in HG J68 two weeks after receiving the exercise sheet. Your solutions will usually be corrected and returned in the following exercise class or, if not collected, returned to the box in HG J68.

exercise sheet due by solutions
Exercise sheet 1 March 19 Solutions 1
Exercise sheet 2 March 29 (Because of easter!) Solutions 2
Exercise sheet 3 April 23 Solutions 3
Exercise sheet 4 May 7 Solutions 4
Exercise sheet 5 May 28 Solutions 5
Exercise sheet 6 -

Exercise classes

The first exercise class will be in the second week of the semester, monday 26th of February.

timeroomassistantlanguage
Mo 12-13HG F 26.3Dante BonolisEnglish

Literature

Primary References:
  1. Robin Hartshorne: Algebraic Geometry, Graduate Texts in Mathematics, Springer.
  2. David Eisenbud, Joe Harris: The Geometry of Schemes, Graduate Texts in Mathematics, Springer.
  3. Enrico Bombieri: http://www.numdam.org/item/SB_1972-1973__15__234_0
  4. Joseph Silverman: The Arithmetic of Elliptic Curves, Graduate Texts in Mathematics, Springer.
  5. Joe Harris: Algebraic Geometry, A First Course, Graduate Texts in Mathematics, Springer.
  6. J. Matousek: https://kam.mff.cuni.cz/~matousek/polychap.pdf
Secondary References:
  1. Qing Liu: Algebraic Geometry and Arithmetic Curves, Oxford Science Publications.
  2. Ulrich Görtz and Torsten Wedhorn: Algebraic Geometry I, Advanced Lectures in Mathematics, Springer.
  3. Siegfried Bosch: Algebraic Geometry and Commutative Algebra (Springer 2013).
Further Readings
  1. Ravi Vakil, Foundations of Algebraic Geometry, http://math.stanford.edu/~vakil/216blog/
  2. Jean Gallier and Stephen S. Shatz, Algebraic Geometry, http://www.cis.upenn.edu/~jean/algeom/steve01.html
  3. J.S. Milne, Algebraic Geometry, http://www.jmilne.org/math/CourseNotes/AG.pdf
  4. Günter Harder: Algebraic Geometry 1 & 2.
  5. I. R. Shafarevich, Basic Algebraic geometry 1 & 2, Springer-Verlag.
  6. Alexandre Grothendieck et al.: Elements de Geometrie Algebrique EGA.
  7. Saunders MacLane: Categories for the Working Mathematician, Springer-Verlag.