Student Algebraic Geometry Seminar


Title: A brief introduction to jet schemes


Abstract: In the previous talks we learned about multiplier ideals and log canonical thresholds, and about their relation to singularities. In this talk, we will introduce jet schemes and use them to present another way to measure singularities. We will start by presenting the definition and basic properties of jet schemes, and then we will state some of Professor Mustata's theorems on singularities and jet schemes. In the rest of the talk, we will present several examples to illustrate these statements and recover some of the results in Paul's talk.