This is the information page for SFU reading group about moduli space for graduate students. (Last updated: 2026 November 8)
We will mainly follow the lecture notes by Victoria Hoskins (https://www.math.ru.nl/~vhoskins/moduli_and_GIT.html). Other supplementary materials you may find helpful:
Topics in these materials may be discussed on demand.
Suggested prerequisite / co-requisite:
The tentative meeting plan is below. If you have any question, please contact Karolyn So (wsa57 at sfu dot ca) or Chi Ki Ngai (ckn10 at sfu dot ca).
| Date | Content | Supplementary material | Notes | Person in charge |
|---|---|---|---|---|
| Jul 10 | Introduction and scheme theory | No reading needed beforehand | Notes | Chi Ki |
| Jul 17 | Functor of points, moduli problems and moduli functors | Sections 2.1-2.2 of the main lecture notes | Notes | Karolyn |
| Jul 24 | Fine and coarse moduli spaces, pathologies, constructing moduli spaces | Sections 2.3-2.6 of the main lecture notes | Notes | Chi Ki |
| Jul 31 | Algebraic groups and algebraic actions | Sections 3.1-3.3 of the main lecture notes (Up to Definition 3.16) (covered up to Definition 3.13) | Notes | Pijush |
| Aug 7 | Categorical quotients, good quotients and geometric quotients | Sections 3.3-3.5 of the main lecture notes (From Example 3.17) | Notes | Young |
| Aug 14 | Hilbert’s 14th problem I: unipotent and reductive groups | Sections 3.6-4.2 of the main lecture notes | Notes | Karolyn |
| Break | Resume in mid-September | – | – | – |
| Sep 24 | Review on moduli spaces | Recommend reading previous materials | Notes | Pijush |
| Oct 1 | Hilbert’s 14th problem II: Weyl’s unitary trick, Reynolds operators and Nagata’s Theorem | Sections 4.2-4.5 of the main lecture notes (From Proposition 4.18 to Remark 4.28) | No notes | Young |
| Oct 8 | The affine GIT quotient: it is a good quotient and restricts to a geometric quotient on the stable set | Sections 4.5-4.6 of the main lecture notes (From Lemma 4.29) | Notes (Up to 4.5) | Chi Ki |
| Oct 15 | Stable points and Exercise on calculating ring of invariants | Section 4.6 of of the main lecture notes and Exercise sheet 6 (Q1, Q3) from the main lecture notes series | Notes, Demo Macaulay2 code | Chi Ki |
| Oct 22 | The projective GIT quotient: (semi)stability, S-equivalence and polystability | Sections 5.1-5.2 of the main lecture notes | Notes, Demo Macaulay2 code | Pijush |
| Oct 29 | The Hilbert-Mumford criterion for (semi)stability I | Sections 6.1-6.2 of the main lecture notes | Notes | Chi Ki |
| Nov 5 | Exercises on the Hilbert-Mumford criterion for (semi)stability | Exercise sheet 10 | Notes, Demo Macaulay2 code | Karolyn |
| Nov 12 | Exercises on projective GIT and (semi)stable sets | Exercise sheet 8, Exercise sheet 9 | Pijush | |
| Nov 19 | Moduli of projective hypersurfaces I (General theory) | Sections 7.1-7.3 of the main lecture notes | TBD | |
| Nov 26 | Moduli of projective hypersurfaces II (Particular examples) | Sections 7.4-7.5 of the main lecture notes | TBD | |
| Dec 3 | Crash course on sheaf cohomology | Sections 8.1-8.3 of the main lecture notes | TBD |