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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

29 votes
3 answers
3k views

Why are derived categories natural places to do deformation theory?

It seems to me that a lot of people do deformation theory (of schemes, sheaves, maps etc) in derived category (of an appropriate abelian category). For example, the cotangent complex of a morphism $f: …
Daniel's user avatar
  • 349
5 votes
0 answers
370 views

Deformation theory with a view toward GW theory and DT theory

I am studying GW theory (and DT theory) in algebraic geometry. I now understand the heuristic "Aut, Def, Obs" argument written in Mirror Symmetry book (by Hori et al.), but it is too hard for me to re …
Daniel's user avatar
  • 349