Homework Problems:
Taking notes:
A small part of the grade is based on note taking for a single class. You choose which class you are going to take notes in. You communicate to me this choice either by email or in person, at least one day in advance. You submit your notes up to 10 days later. Here is an overleaf template for the notes: notes.tex)
End of semester presentations:
Each of you will choose a class of varieties from the list below and do a 30 minute presentation to give the audience the definition of your chosen variety and their many geometric and algebraic properties. To learn about this varieties, first look for them in Joe Harris’ book “Introduction to Algebraic Geometry” where they appear frequently. You may also want to consult other algebraic geometry books or notes. Chose your variety by November 12th, 2024. Once you chose, tell me about it. Two weeks before your presentation, send me an email with an outline of the content of your presentation.
- Secant varieties
- Rational normal curves
- Veronese varieties
- Segre varieties
- Rational normal scrolls
- Grassmanians
- Determinantal varieties
- Toric Varieties
- Sets of points in projective space
- Blow-ups (See Harthsorne p. 28)
W1.Lecture 1-19.09
Introduction. Bezout’s Theorem, affine varieties Ch1.S1,S2.
W2.Lecture 2-24.09
Affine varieties. Ch1.S1.S2. Variety of an ideal. Ideal of a set.
W2.Lecture 3-26.09
Affine varieties. Ch1.S3. Computing with polynomials. LectureNotes Irreducible topological space.
W3.Lecture 4-01.10
Affine varieties. Ch1.S3, Ch1.S4.
W4.Lecture 5-03.10 -
Affine varieties. Finish Ch1.S4. Start of morphisms.
W4.Lecture 6-08.10
Discussion of Homework. Beginning of projective spaces.
W5.Lecture 7-10.10
Continuation of projective spaces. Beginning of sheaves.
W5.Lecture 8-15.10
Schemes
W6.Lecture 9-17.10
Schemes