1
Deformations of Nodal Curves
Node smoothing, the local deformation sheaf, and the count 3g-3+n
2
Moduli Space of Stable Maps
Moduli of stable maps, Deligne-Mumford stacks, virtual dimensions, and convex targets
3
Perfect Obstruction Theory
Perfect obstruction theory, virtual fundamental class, intrinsic normal cone, localized Euler class