18.725 | Fall 2003 | Graduate

Algebraic Geometry

Lecture Notes

The lecture notes are courtesy Moses Liskov, a student in the class. Used with permission.

LEC # TOPICS
1 Introduction (PDF)

First Goal

2 Recap of Last Time (PDF)

Irreducible Components

Projective Space

3 Projective Space (cont.) (PDF)
4 Projective Space (cont.) (PDF)

Topological Diversion

Sheaves

5 Presheaves (PDF)

Back to Algebraic Geometry

6 Review of things not covered enough (Topics: Fibers, Morphisms of Sheaves) (PDF)

Back to Work

Morphisms

Varieties

7 Homework Review (PDF)

Back to Varieties

8 Projective Varieties (PDF)
9 A Review on Projective Varieties (PDF)

Product of Varieties

10 Applications (PDF)
11 Recap on the Applications (PDF)

Next Definition of Variety

Dimension

12 Homework 5 Problem (PDF)

Dimension

Future Applications

13 Back to Dimension (PDF)

Krull Dimension

14 Fibers of Morphisms (PDF)
15 Fiber Products (PDF)

Back to the Theorem

Complete Varities

16 Completeness (PDF)

Complex Topology

17 Chow’s Lemma (PDF)

Analytic Spaces

18 Curves (PDF)
19 What is Next? (PDF)

How to Study Curves

Course Info

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Fall 2003
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Lecture Notes
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