Moduli of Curves (Fall 2014)
Course outline
Week 1: Functors, representability, and the Grassmannian (
Notes and exercises
)
Week 2: Flatness, Hilbert scheme (
Exercises
).
Week 3: Infinitesimal lifting, smoothness, deformations, obstructions. (Notes:
Sept 16
,
Sept 18
.)
Week 4: Spaces of morphisms, outline of the construction of Hilb (Notes:
Sept 23
,
Sept 25
,
Exercises
)
Week 5: Uniform
m
lemma, flattening stratifications (
Sept 30–Oct 2
)
Week 6: Moduli of curves, fine/coarse moduli spaces (
Oct 7–9
)
Week 7: Irreducibility of
M
g
, Picard–Lefschetz (Notes:
Oct 14
,
Oct 16
)
Week 8: Stacks (Notes:
Oct 21
,
Oct 23
)
Week 9: Algebraic stacks,
M
g
(Notes:
Oct 28
,
Oct 30
)
Week 10: Sheaves on algebraic stacks, Picard group of
M
1,1
(Notes:
Nov 6
)
Week 11: Separated/proper morphisms, coarse spaces, Deligne–Mumford compactification of
M
g
, stable reduction (Notes:
Nov 11
,
Nov 13
,
Exercises on stable reduction
)
Week 12: Local structure of
M
g
, deformation theory (Notes:
Nov 18
,
Nov 20
)
Week 13: Line bundles and divisor classes on
M
g
(Notes:
Nov 25
)
Week 14: Mumford's relation, canonical class, ample/effective divisors (Notes:
Dec 2
)