
MAT 589 Syllabus
Introduction to Algebraic Geometry
Spring 2017

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 23
Summary of the classical ideal—variety correspondence.
 Thursday, January 25
Summary of commutative ring theory.
 Tuesday, January 31
Sheaves. Section II.1
 Thursday, February 2
Locally ringed spaces. Section II.2
Problem Set 1
due in lecture.
 Tuesday, February 7
Affine schemes and Proj. Section II.3.
 Thursday, February 9
Properties of morphisms. Various sections.
 Tuesday, February 14
Fiber products and separatedness. Section II.4.
Problem Set 2
due in lecture.
 Thursday, February 16
Valuative criteria. Section II.4.
 Tuesday, February 21
Proper morphisms and Chow's Lemma. Section II.4.
Problem Set 3
due in lecture.
 Thursday, February 23
Quasicoherent sheaves. Section II.5.
 Tuesday, February 28
More about quasicoherent sheaves. Section II.5.
Problem Set 4
due in lecture.
 Thursday, March 2
Quotients and Proj.
 Tuesday, March 7
Projective morphisms and divisors. Sections II.6 and II.7.
Problem Set 5
due in lecture.
 Thursday, March 9
Differentials. Section II.8.
 Tuesday, March 21
Ample and very ample divisors. Section II.7.
Problem Set 6
due in lecture.
 Thursday, March 23
Homological algebra. Section III.1.
 Tuesday, March 28
Properties of derived functors. Section III.2.
Problem Set 7
due in lecture.
 Thursday, March 30
Cohomology of quasicoherent sheaves on a Noetherian affine. Section III.3.
 Tuesday, April 4
Čech cohomology. Section III.4.
Problem Set 8
due in lecture.
 Thursday, April 6
Čech and sheaf cohomology. Section III.4.
 Tuesday, April 11
Cohomology on projective space. Section III.5.
Problem Set 9
due in lecture.
 Thursday, April 13
Duality on projective space. Section III.5.
 Tuesday, April 18
Serre duality I. Sections III.6 and III.7.
Problem Set 10
due in lecture.
 Thursday, April 20
Serre duality II. Section III.7.
 Tuesday, April 25
Lefschetz theorems and differentials. Various sections.
Problem Set 11
due in lecture.
 Thursday, April 27
Dualizing and canonical sheaves. Section III.7.
 Tuesday, May 2
Zariski's Main Theorem. Section III.11.
Problem Set 12
due in lecture.
 Thursday, May 4
Semicontinuity and base change. Section III.12.
Back to my home page.
Jason Starr
4108 Math Tower
Department of Mathematics
Stony Brook University
Stony Brook, NY 117943651
Phone: 6316328270
Fax: 6316327631
Jason Starr