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MAT 589 Syllabus
Introduction to Algebraic Geometry
Spring 2020
|
The
schedule for topics covered in lecture is as follows. Please
do
the assigned reading prior to lecture. This will make the lectures
more effective for you.
- Tuesday, January 28
Summary of the classical idealvariety correspondence.
- Thursday, January 30
Summary of commutative ring theory.
- Tuesday, February 4
Sheaves. Section II.1
- Thursday, February 6
Locally ringed spaces. Section II.2
Problem Set 1
due in lecture.
- Tuesday, February 11
Affine schemes and Proj. Section II.3.
- Thursday, February 13
Properties of morphisms. Various sections.
Problem Set 2
due in lecture.
- Tuesday, February 18
Fiber products and separatedness. Section II.4.
- Thursday, February 20
Valuative criteria. Section II.4.
Problem Set 3
due in lecture.
- Tuesday, February 25
Proper morphisms and Chow's Lemma. Section II.4.
- Thursday, February 27
Quasi-coherent sheaves. Section II.5.
Problem Set 4
due in lecture.
- Tuesday, March 3
More about quasi-coherent sheaves. Section II.5.
- Thursday, March 5
Quotients and Proj.
Problem Set 5
due in lecture.
- Tuesday, March 10
Projective morphisms and divisors. Sections II.6 and II.7.
- Thursday, March 12
Differentials. Section II.8.
Problem Set 6
due in lecture.
- Tuesday, March 24
Ample and very ample divisors. Section II.7.
- Thursday, March 26
Homological algebra. Section III.1.
Problem Set 7
due in lecture.
- Tuesday, March 31
Properties of derived functors. Section III.2.
- Thursday, April 2
Cohomology of quasi-coherent sheaves on a Noetherian affine. Section III.3.
Problem Set 8
due in lecture.
- Tuesday, April 7
Čech cohomology. Section III.4.
- Thursday, April 9
Čech and sheaf cohomology. Section III.4.
Problem Set 9
due in lecture.
- Tuesday, April 14
Cohomology on projective space. Section III.5.
- Thursday, April 16
Duality on projective space. Section III.5.
Problem Set 10
due in lecture.
- Tuesday, April 21
Serre duality I. Sections III.6 and III.7.
- Thursday, April 23
Serre duality II. Section III.7.
Problem Set 11
due in lecture.
- Tuesday, April 28
Lefschetz theorems and differentials. Various sections.
- Thursday, April 30
Dualizing and canonical sheaves. Section III.7.
Problem Set 12
due in lecture.
- Tuesday, May 5
Zariski's Main Theorem. Section III.11.
- Thursday, May 7
Semicontinuity and base change. Section III.12.
Problem Set 13
due in lecture.
Back to my home page.
Jason Starr
4-108 Math Tower
Department of Mathematics
Stony Brook University
Stony Brook, NY 11794-3651
Phone: 631-632-8270
Fax: 631-632-7631
Jason Starr