# 10 - Boundedness of Varieties of General Type, 2015

SGU Special Lectures (Algebraic Geometry)

### Boundedness of Varieties of General Type

Christopher Hacon
Kyoto University / Distinguished Visiting Professor
University of Utah / Distinguished Professor

Jun. 10, 12, 17, 19 and 26, 2015
Room127, Graduate School of Science Bldg No 3
Room 420, Research Institute for Mathematical Sciences

Lecture Video

#### Course Description

Varieties of general type are the higher dimensional analog of Riemann surfaces of genus $g\geq 2$. If $X\subset \mathbb P ^N _{\mathbb C}$ is a variety of general type then, by definition, the sections of $H^0(\omega _X^{\otimes m})$ determine a birational map for all sufficiently big integers $m>0$.
In these lectures we will explain recent results on the boundedness of varieties of general type that ultimately lead to the construction of a corresponding moduli space (more precisely to the construction of the KSBA proper functor of log canonically polarized log canonical pairs).