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Algebraic Geometry

Virtual Classes


1. A review of Fulton-MacPherson intersection theory.
2. Cones, normal cones, lci morphisms and reduced cotangent complex.
3. Groupoids, 2-categories and stacks.
4. Deligne-Mumford and Artin algebraic stacks.
5. Abelian cone stacks and derived category; normal cone stack.
6. Perfect obstruction theories and virtual classes.
7. Functorial properties of virtual classes and pullbacks.
8. Gromov-Witten invariants: definition and proof of the
Kontsevich-Manin axioms.


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