Math 620, Fall 2024:
Algebraic Geometry
Meeting: MWF 11:30-12:20 BLOC 110
Office hours Tues. and Wed. 2:30-3:30  or by appointment
Instructor: Joseph (JM) Landsberg

 

 

 
E-mail: jml@math.tamu.edu please include "620" in the subject line when emailing me
 
my cv

 

Prerequisites. Math 653 or permission of the instructor.

Course text.  Basic algebraic geometry I, I. Shafarevich,  third edition, Springer
Course description: This is a first course in algebraic geometry, we will cover Chapters 1,2 and 3 of the text plus additional topics.

 


Grade complaints: If you think a homework  was graded incorrectly you
have one week from the time the graded assignment was returned to you to bring the
issue to the instructor's attention. No complaints after that time will be considered.
  

Grading policy: Weekly homework assignments (100%)
Assignments will usually consist of 3 problems and we will go over them in class the
day they are due. You are encouraged to do additional problems from the book and
are welcome to present them to the class if you like.

Weekly homework assignments and announcements
Due 8/28 (Wed.) :  Section 1: 3,7,9 (optional: 6)
Due 9/4 (Wed.): Section 2: 3,6,13,14
Due 9/13 (Friday): Section 3: 3, 6,7 plus show that GL_n (the set of invertible nxn matrices)  is an affine variety.
Read these notes
Extra credit problems: from notes: 4.10, 4.11, sect. 5: 1,2,4, sect. 6: 1.
Due 9/20 (Friday): Section 4: 3,9,11. Extra credit problems:
Due 9/27: Section 5: 8, section 6: 3,5 notes from 9/13: 5(3), extra credit: notes: 5(5), 6(2), 6(3)
Due 10/9 (Wed.) Section 6: 12, 13 and these two problems, extra credit: from 9/13 notes 5(5).
Optional homework problems to keep you from getting bored the next two weeks
Due 10/23 (Wed.) Sect. II.1.6: 5,6,10,13 (assume deg(X)>1).
Due 11/6 (Wed.)  Sect. II.4: 1,2,3,4,10
Due 11/15 (Fri.) Sect. II.5: 6,8 (in 6 assume n>2), II.6: 2, plus
compute the tangent cone to the variety of rank at most n-1 nxn matrices at a rank s<n-1 matrix.
Due Dec. 5 (Thurs) Sect III.1: 1,6,8, 14

 
 
Policy regarding absences related to injury or illness: All such absences will be excused
if sufficient documentation is provided as per University policy and
the instructor will help the student make up any missed material.
 

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