The topic of MAT4230 - ¡­

The topic of MAT4230 - Algebraic geometry III will be Moduli spaces and Hilbert schemes. We will start with some classical examples of parameter varieties - linear systems, Grassmannians, Chow varieties, and pass to Hilbert schemes; the main objects we want to parameterize are curves (and points). Then we will give a gentle introduction to algebraic spaces and stacks, before looking more carefully at the moduli space of stable (pointed) curves. The underlying motivation is "curve counting" on surfaces and threefolds, also known as the study of numerical invariants as in Gromov-Witten and Donaldson-Thomas theory.