Geometry of Schemes

Practical Information

• Time slot: Tuesdays, 13.30-15.30


• Location: HG01.057


• Main source: David Eisenbud, Joe Harris, The Geometry of Schemes, Springer (2000).


• Background sources:
  • Kenji Ueno, Algebraic Geometry 1: From algebraic varieties to schemes, Translations of Mathematical Monographs 185, AMS (1999).
  • Robin Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, Springer (1977).
  • Serge Lang, Algebra, Graduate Texts in Mathematics, Springer (2002).
  
  
• Participants: Noud Aldenhoven, Jord Boeijink, Dion Coumans, Robert Furber, Sam van Gool, Roberta Iseppi, Bert Lindenhovius, Maarten van Pruijssen, Sander Rieken, Sander Wolters.

Schedule

• Tuesday 4 October, 13.30-15.30, Sander Wolters: Affine varieties and their relation to finitely generated integral domains over an algebraically closed field, I.
  
  Prerequisites: Only the very basics of ring theory. Know what a commutative ring with unit, a prime ideal, an integral domain and a(n algebraically closed) field are.
  
  Reading: Ueno, sections 1.1-1.3, Hartshorne, parts of sections 1.1 and 1.3, some elementary commutative algebra taken from Lang.


• Tuesday 11 October, 13.30-15.30, Sander Wolters: Affine varieties and their relation to finitely generated integral domains over an algebraically closed field, II.


• Tuesday 18 October, 13.30-14.30, Sander Wolters: Affine varieties and their relation to finitely generated integral domains over an algebraically closed field, III.


• Tuesday 18 October, 14.30-15.30 Sander Rieken: Affine schemes, I.
  
  Reading: Eisenbud/Harris, Sections I.1.1 and I.1.2.


• Tuesday 25 October, 10.00-12.00, Sander Rieken: Affine schemes, II.

Reading: Eisenbud/Harris, Sections I.1.3 and I.1.4.


• Monday 31 October, 11.00-13.00, Noud Aldenhoven: Schemes in General.

Reading: Eisenbud/Harris, Sections I.2.1 and I.2.2.


• Tuesday 1 November, 13.30-15.30, Sam van Gool: Exercises on Sheaves.
  
  Exercises: Eisenbud/Harris, Section I.1.3: Exercises I-5, (I-6), I-7, I-8*, I-9, I-10, I-11*, I-13*, I-15*.
  I-6: only for those who know about vector bundles.
  Starred exercises are not necessarily more difficult, but of a more theoretical nature. The other exercises are important examples, too.
  
  
• Tuesday 8 November, 13.30-15.30, Dion Coumans and Sam van Gool: The duality theorem for affine schemes.

Reading: Eisenbud/Harris, Section I.2, at least up till Corollary I-41.


• Tuesday 13 December, 13.30-15.30, Maarten Solleveld: Examples and constructions of schemes.


• Tuesday 20 December, 13.30-15.30, Maarten Solleveld: Examples and constructions of schemes, part II.


• Tuesday 17 January, 13.30-15.30, Maarten van Pruijssen: Projective Schemes.
  
  Reading: Eisenbud/Harris, parts from Chapter III.


• Tuesday 24 January, 13.30-15.30, Roberta Iseppi: Classification of curves, part I.


• Tuesday 31 January, 13.30-15.30, Roberta Iseppi: Classification of curves, part II.


• Tuesday 7 February, 13.30-15.30, Joseph Steenbrink: Why schemes? Slides




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Last modified: 7 February 2012.