# Math 763 -- Algebraic Geometry I

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# Fall 2019

## Homework assignments

- Homework 1, due Thursday, September 19th.
- Homework 2, due Thursday, September 26th.
- Homework 3, due Tuesday, October 8th.
- Homework 4, due Thursday, October 17th.
- Homework 5, due Thursday, October 31st.
- Homework 6, due Thursday, November 7th.
- Homework 7, due Thursday, November 14th.
- Homework 8, due Thursday, November 21st.
- Homework 9, due Thursday, December 5th.

## Course description

This is a first course in algebraic geometry. While there are no formal prerequisites beyond a knowledge of the material covered in the first-year algebra and geometry sequence, familiarity with some basic commutative algebra will be helpful. The rough outline of the course is as follows (subject to change):

- Affine and projective varieties.
- Morphisms and rational maps.
- Local properties: smoothness and dimension. Tangent space.
- Divisors.
- Low-dimensional varieties: curves and surfaces. Blow-ups.
- The Riemann-Roch Theorem.

Here is a more detailed lecture-by-lecture list of topics that I covered in the past, of course, this is all subject to change.

## Handouts

## References

- Shafarevich, Basic Algebraic Geometry.
- Algebraic Geometry (online notes) by Milne.
- Hartshorne, Algebraic Geometry, Chapter I (this is more advanced, so does not quite match the content).
- Here is a discussion on MathOverflow with more books on algebraic geometry, but most of them are going to be too advanced.
- Here are notes from the last time I taught this course. These were taken in class, so

there are probably typos.

## Information for students

**Instructor**: Dima Arinkin**Office Hours**: Tuesday 3-4pm, Wednesday 2-2:45pm, and by appointment in VV 603**Lectures**: TuTh 11am-12:15pm, VV B129**Grade**: There will be weekly homework assignments, but no exams in this course.