Curve Counting via Stable Pairs in the Derived Category

  title={Curve Counting via Stable Pairs in the Derived Category},
  author={Rohit Pandharipande and Richard P. Thomas}
For a nonsingular projective 3-fold X, we define integer invariants virtually enumerating pairs (C, D) where C ⊂ X is an embedded curve and D ⊂ C is a divisor. A virtual class is constructed on the associated moduli space by viewing a pair as an object in the derived category of X. The resulting invariants are conjecturally equivalent, after universal transformations, to both the Gromov-Witten and DT theories of X. For Calabi-Yau 3-folds, the latter equivalence should be viewed as a wall… CONTINUE READING
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