Playlist - Classification theory of algebraic varieties

The classification of algebraic varieties is at the heart of algebraic geometry. With roots in the ancient world the theory saw great advances in dimensions one and two in the 19th century and the first half of 20th century. It was only in the 1970-80's that a general framework was formulated, and by the early 1990's a satisfactory theory was developed in dimension 3. The last 30 years has seen great progress in all dimensions.

In the first lecture I will try to give a historical perspective and discuss the theory in general terms. I will explain how the theory is based on birational transformations and moduli considerations.

The classification of algebraic varieties is at the heart of algebraic geometry. With roots in the ancient world the theory saw great advances in dimensions one and two in the 19th century and the first half of 20th century. It was only in the 1970-80s that a general framework was formulated, and by the early 1990s a satisfactory theory was developed in dimension 3. The last 30 years has seen great progress in all dimensions.

In the second lecture I will discuss log Calabi-Yau fibrations. This is a class of spaces which includes Fano and Calabi-Yau varieties and their local counterparts. They are of great importance in the classification theory and well beyond.

The classification of algebraic varieties is at the heart of algebraic geometry. With roots in the ancient world the theory saw great advances in dimensions one and two in the 19th century and the first half of 20th century. It was only in the 1970-80s that a general framework was formulated, and by the early 1990s a satisfactory theory was developed in dimension 3. The last 30 years has seen great progress in all dimensions.

In the third lecture I will talk about generalised pairs. This is a recently developed notion generalising the notions of varieties and pairs. It has found many applications and fits well into the classification theory.