Math 248B, Spring 2026

Spring Quarter 2026

University of California Davis
Department of Mathematics

This is the website for the course MAT248B at the Department of Mathematics at UC Davis. The course will have the textbook Algebraic Geometry by R. Hartshorne. The goal of the course is to develop the ability to manipulate sheaves and perform homological computations with them to acquire an understanding of the geometry of schemes. The course will first focus on applications to curves and surfaces, and gear towards the derived setting in the second part. See also the Department Syllabus.

Course Information

Lectures: MWF at 3:10pm in Social Sciences 70. Attendance not mandatory.

Textbook: Algebraic Geometry by R. Hartshorne.

Office Hours: The office hours of Professor Casals (casals--at--ucdavis.edu) are Fridays 2:00-3:00pm at MSB 3214. Always feel free to ask after class.

Grade: The grade will be determined by Problem Sets and a Final Project, each part with a 50% weight.

Problem Sets: Weekly assignments due on Fridays at 3pm, submitted through Gradescope.

Math Diaries

Monday Apr 3: Introduction to MAT-248B.

Geometric intuition through the lens of homological algebra.
Instances of applications: Riemann-Roch and Serre's intersection formula.
Necessary ingredients to use sheaves in algebraic geometry.
First rigorous definitions and motivating examples.

Textbook Reading (Mar 30): Chapter I.

Further Resources

Books: The book "Algebraic Geometry II" from the Encyclopaedia of Mathematical Sciences (EMS, volume 35) is a good resource, especially Chapter II by V.I. Danilov.
The book "Lectures on Curves on an Algebraic Surface" by D. Mumford abounds with mathematical pearls. The book "The Rising Sea" (Chapters V and VI) by R. Vakil could be helpful as well.