Boundedness of Varieties of General Type

Lecture 1 Christopher HACON

Course Description

Varieties of general type are the higher dimensional analog of Riemann surfaces of genus \(g \geq 2\). If \(X \subset \mathbb{ P }^N_C\) is a variety of general type then, by definition, the sections of \( H^0(\omega^{\otimes m}_X) \) determine a birational map for all sufficiently big integers \( m \gt 0\).

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).