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.
MSC Code: