Algebraic curves

Instructor: Tsung-Ju Lee（李宗儒）

Term: Fall（秋季）

Location: 數學系館

Lecture Time: Tuesdays 11:10AM - 12:00PM and Fridays 10:10AM - 12:00PM

Course Overview

This course provides a comprehensive introduction to algebraic curves.

Prerequisites

Undergraduate Algebra (1)(2), Linear Algebra (1)(2).

Textbooks

[F] Algebraic curves, W. Fulton.
[H] Algebraic geometry, R. Hartshorne.

Schedule

Week	Date	Topic	Materials
1	Sep 8, Sep 11	Affine algebraic sets Affine algebraic sets.	[F] Chapter 1
2	Sep 15, Sep 18	Affine varieties Affine varieties.	[F] Chapter 2
3	Sep 22, Sep 25	Local properties of plane curves Local properties of plane curves (I).	[F] Chapter 3
4	Sep 29, Oct 2	Local properties of plane curves Local properties of plane curves (II).	[F] Chapter 3
5	Oct 6, Oct 9	Projective varieties and projective plane curves Projective varieties and projective plane curves.	[F] Chapters 4, 5
6	Oct 13, Oct 16	Morphisms and rational maps Morphisms and rational maps.	[F] Chapter 6
7	Oct 20, Oct 23	Resolution of singularities Resolution of singularities.	[F] Chapter 7
8	Oct 27, Oct 30	The Riemann--Roch theorem The Riemann–Roch theorem.	[F] Chapter 8
9	Nov 3, Nov 6	Midterm Midterm.
10	Nov 10, Nov 13	Divisors, line bundles, and the Riemann--Hurwitz formula Divisors and line bundles; the Riemann–Hurwitz formula (I).	[H] Chapter IV, Sections 1-2
11	Nov 17, Nov 20	The Riemann--Hurwitz formula The Riemann–Hurwitz formula (II).	[H] Chapter IV, Section 2
12	Nov 24, Nov 27	Projective embeddings Projective embeddings.	[H] Chapter IV, Section 3
13	Dec 1, Dec 4	Elliptic curves Elliptic curves (I).	[H] Chapter IV, Section 4
14	Dec 8, Dec 11	Elliptic curves Elliptic curves (II).	[H] Chapter IV, Section 4
15	Dec 15, Dec 18	Elliptic curves Elliptic curves (III).	[H] Chapter IV, Section 4
16	Dec 22, Dec 25	Canonical embeddings and higher genus curves Canonical embeddings and higher genus curves (I).	[H] Chapter IV, Section 5
17	Dec 29, Jan 1	Canonical embeddings and higher genus curves Canonical embeddings and higher genus curves (II).	[H] Chapter IV, Sections 5-6
18	Jan 5, Jan 8	Final Exam/Report Final exam/report.