# Finding Rational Curves

# Finding Rational Curves

Charlie Stibitz , Princeton University

Fine Hall 314

Rational curves are one of the most basic objects to look at on an algebraic variety, but they have a large impact on the geometric structure of the variety in which they sit. In this talk we will talk about what are rational curves, why they are useful, and how they are found. In particular we will discuss their role in birational geometry and look at Mori's proof of the bend and break theorem, used to prove certain rational curves exist on an algebraic variety.