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Browse materialsMIT 18.725 · Fall 2003

Algebraic Geometry

Subjects: Algebra · Geometry · Mathematics

Art: Anonymous painter,15th century, Westerner and Arab practicing geometry 15th century manuscript, 15th… · Public domain

Instructor: Prof. Martin Olsson
Term: Fall 2003
Level: Graduate
What's inside: 1 lecture note · 1 reading · 30 other files · 3 web pages
Materials open: MIT OCW

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18.725 · Fall 2015 · Study here
18.725 · Fall 2003 · Study here (this version)

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About this course

Source: MIT OpenCourseWare 18.725 Algebraic Geometry, Fall 2003, Prof. Martin Olsson — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.

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Before you start

Prerequisites are not listed here. Check MIT's own syllabus for this course.

How this course was organized

What's here, and what isn't

A lecture sequence of 19 items is confirmed. Assignment and exam materials exist too, but MIT's own order for them could not be verified, so they're shown as materials below rather than a sequence.

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Materials by section

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Lecture Notes

19 files

Assignments

11 files

MIT OpenCourseWare, Prof. Martin Olsson, 18.725 Algebraic Geometry, Fall 2003.

License: CC BY-NC-SA 4.0 · Edition: Fall 2003 · Open the original course on OCW ↗

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Algebraic Geometry

Before you start

What's here, and what isn't

Not included here

Materials by section

Lecture Notes

Assignments

Lecture 1: Introduction First Goal

Lecture 2: Recap of Last Time Irreducible Components Projective Space

Lecture 3: Projective Space (cont.)

Lecture 4: Projective Space (cont.) Topological Diversion Sheaves

Lecture 5: Presheaves Back to Algebraic Geometry

Lecture 6: Review of things not covered enough (Topics: Fibers, Morphisms of Sheaves) Back to Work Morphisms Varieties

Lecture 7: Homework Review Back to Varieties

Lecture 8: Projective Varieties

Lecture 9: A Review on Projective Varieties Product of Varieties

Lecture 10: Applications

Lecture 11: Recap on the Applications Next Definition of Variety Dimension

Lecture 12: Homework 5 Problem Dimension Future Applications

Lecture 13: Back to Dimension Krull Dimension

Lecture 14: Fibers of Morphisms

Lecture 15: Fiber Products Back to the Theorem Complete Varities

Lecture 16: Completeness Complex Topology

Lecture 17: Chow’s Lemma Analytic Spaces

Lecture 18: Curves

Lecture 19: What is Next? How to Study Curves