Math 764 -- Algebraic Geometry II

Spring 2020

Course description

This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.

We will start with the Riemann-Roch Theorem and the related topics (divisors, projective embeddings). Then we will go over basic properties of sheaves, and define schemes and morphisms of schemes.

References

• Hartshorne, Algebraic Geometry.
• Shafarevich, Basic Algebraic Geometry.
• Ravi Vakil’s online notes, The Rising Sea.
• Notes by Daniel Hast for this course (Algebraic Geometry II) in 2015.

Information for students

• Instructor: Dima Arinkin
• Office Hours: Monday 2-3pm and by appointment in VV 603
• Lectures: MWF 9:55-10:45am, VV B131
• Grade: There will be weekly homework assignments, but no exams in this course.

Homework assignments

• Homework 1, due Wednesday, February 12th.
• Homework 2, due Wednesday, February 19th.
• Homework 3, due Wednesday, February 26th.
• Homework 4, due Wednesday, March 4th.
• Homework 5, due Wednesday, March 25th.

Spring 2017

Homework assignments

Course description

This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.

In the beginning of the course, we will go over basic properties of sheaves. We will then define schemes and morphisms of schemes, and study various classes of morphisms. Time permitting, I hope to discuss more interesting topics, such as (quasi)coherent sheaves on schemes and moduli spaces.

References

• Hartshorne, Algebraic Geometry.
• Shafarevich, Basic Algebraic Geometry.
• Ravi Vakil’s online notes, The Rising Sea.
• Notes by Daniel Hast for this course (Algebraic Geometry II) in 2015.