**Instructor:** Evan
Bullock

**Office: **Herman Brown 408

**Office Hours:** Wednesday 3:30-5:00pm, Thursday 1:30-3:00pm, or by
appointment.

**Email:**

**Time:** 01:00PM - 01:50PM MWF

**Location:** HB 453

**Textbook: ** Shafarevich, Basic
Algebraic Geometry I, available from the campus
store

TA: Letao Zhang

For those not familiar with tensor products, I have written a brief summary of the definition of the tensor product (over a field). For more information, including the more general definition for modules, see the section from Atiyah & MacDonald or from Dummit & Foote about tensor products.

Here's the section on symmetric
and alternating tensors, also from Dummit
& Foote.

Algebraic Geometry: A First Course, by Joe Harris, has a very nice treatment of Veronese and Segre varieties and Grassmannians.

I've written some lecture notes on Grassmannians.I've collected some additional problems on dimension.

Homework 1, due Friday, January 21

Homework 2, due Friday, January 28

Homework 3, due Monday, February 7

Homework 4, due Friday, February 11

Homework 5, due Friday, February 18

Homework 6, due Friday, March 11

Homework 7, due Wednesday, March 23 (see notes)

Homework 8, due Friday, April 1 (hint added to #7)

Homework 9, due Friday, April 8 (hints added to #1 and #6, hint in #2a replaced with a hint that will be more helpful in part b)

Homework 10, due Friday, April 15 (hint added to #6b)

Homework 11, due Friday, April 22 (extra credit problem added)

Homework will be assigned weekly, due on Fridays unless announced otherwise. Homework will be very important in this class, and you should you work on every assigned problem: in some cases, results developed in the homeworks may be used in class and likewise some results may be stated without proof in class with the proof left to you on the homework.

I encourage you to talk to other students about the homework problems, but you must write up your own solutions and they should reflect your own understanding.

If you'd like to typeset your homeworks on a computer, I would strongly suggest learning to use L

The topic of the course is algebraic varieties (common zero sets of polynomial equations) in affine and projective space.

Topics may include: plane algebraic curves, Hilbert's
Nullstellensatz, regular and rational maps, products of
quasi-projective varieties and the Segre embedding, completeness of
projective varieties, dimension theory, degree, Bézout's theorem,
tangent space and tangent cone, blow-ups and resolution of
singularities, Grassmannians and the Plücker embedding.

Math 463/563, or equivalent, is a prerequisite for this class: students should be familiar with rings, fields, and Galois theory.

Midterm Exam 1, due Friday, February 25 (solutions to selected problems)

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