# Intersection Theory

Friday, April 13, 2007 - 9:00am - 10:30am

EE/CS 3-180

Jessica Sidman (Mount Holyoke College)

Intersection theory is a big subject that has played an important role in

algebraic geometry, and any attempt at a comprehensive introduction in 90

minutes would surely fail. With this in mind, I have decided instead to

attempt to convey some of the beauty and flavor of intersection theory by

way of discussing a few concrete classical examples of intersection theory

on surfaces.

The material in the talk is covered in almost any text in algebraic

geometry. There are many approaches to finding 27 lines on a cubic

surface. If one wishes to see a more rigorous version of the presentation

given in this talk, then please see Hartshorne's treatment in Chapter V.4

of the book cited in the refereces. Chapter V of Hartshorne's book is a

very nice introduction to intersection theory on surfaces. For a more

general orientation in the subject with good historical context, one might

wish to read Fulton's Introduction to intersection theory in algebraic

geometry. Fulton's other book cited in the references is the standard in

the subject, and the other texts listed offer additional points of view.

algebraic geometry, and any attempt at a comprehensive introduction in 90

minutes would surely fail. With this in mind, I have decided instead to

attempt to convey some of the beauty and flavor of intersection theory by

way of discussing a few concrete classical examples of intersection theory

on surfaces.

The material in the talk is covered in almost any text in algebraic

geometry. There are many approaches to finding 27 lines on a cubic

surface. If one wishes to see a more rigorous version of the presentation

given in this talk, then please see Hartshorne's treatment in Chapter V.4

of the book cited in the refereces. Chapter V of Hartshorne's book is a

very nice introduction to intersection theory on surfaces. For a more

general orientation in the subject with good historical context, one might

wish to read Fulton's Introduction to intersection theory in algebraic

geometry. Fulton's other book cited in the references is the standard in

the subject, and the other texts listed offer additional points of view.

MSC Code:

14C17