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 stack, virtual dimension, convex targets
3
Refined Gysin Morphism
Refined Gysin homomorphisms, excess intersection, and diagonal intersection of virtual classes
4
Perfect Obstruction Theory
Perfect obstruction theory, virtual fundamental class, intrinsic normal cone, localized Euler class