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Browse materialsMIT 18.727 · Spring 2006

Topics in Algebraic Geometry: Intersection Theory on Moduli Spaces

Subjects: Algebra · Geometry · Mathematics

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

Instructor: Dr. Izzet Coskun
Term: Spring 2006
Level: Graduate
What's inside: 1 lecture note · 1 reading · 10 other files · 3 web pages
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Source: MIT OpenCourseWare 18.727 Topics in Algebraic Geometry: Intersection Theory on Moduli Spaces, Spring 2006, Dr. Izzet Coskun — 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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MIT OpenCourseWare, Dr. Izzet Coskun, 18.727 Topics in Algebraic Geometry: Intersection Theory on Moduli Spaces, Spring 2006.

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Topics in Algebraic Geometry: Intersection Theory on Moduli Spaces

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Lecture Notes

Study Materials

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Lecture 1: Introduction to Moduli Spaces

Lecture 2: Introduction to Grassmannians

Lecture 3: Enumerative Geometry using Grassmannians, Pieri and Giambelli

Lecture 4: Littlewood - Richardson Rules and Mondrian Tableaux

Lecture 5: Introduction to Hilbert Schemes

Lecture 6: The Construction of Hilbert Schemes and First Examples

Lecture 7: Enumerative Geometry using Hilbert Schemes: Conics in Projective Space

Lecture 8: Local Properties of Hilbert Schemes: Mumford’s Example

Lecture 9: An Introduction to G.I.T.

Lecture 10: The Hilbert-Mumford Criterion and Examples of G.I.T. Quotients

Lecture 11: The Construction of the Moduli Space of Curves I

Lecture 12: The Construction of the Moduli Space of Curves II

Lecture 13: The Cohomology of the Moduli Space of Curves: Harer’s Theorems

Lecture 14: The Euler Characteristic of the Moduli Space

Lecture 15: Keel’s Thesis

Lecture 16: The Second Cohomology of the Moduli Space

Lecture 17: The Picard Group of the Moduli Functor

Lecture 18: Divisors on the Moduli Space

Lecture 19: Brill-Noether Theory and Divisors of Small Slope

Lecture 20: The Moduli Space of Curves is of General Type when g > 23

Lecture 21: An Introduction to the Kontsevich Moduli Space

Lecture 22: Enumerative Geometry and Gromov-Witten Invariants

Lecture 23: The Picard Group of the Kontsevich Moduli Space

Lecture 24: Vakil’s Algorithm for Counting Rational Curves in Projective Space

Lecture 25: The Ample and Effective Cones of the Kontsevich Moduli Space