Symplectic surgery and Gromov-Witten invariants of Calabi-Yau 3-folds I

Details Symplectic surgery and Gromov-Witten invariants of Calabi-Yau 3-folds I Symplectic surgery and Gromov-Witten invariants of Calabi-Yau 3-folds I

1998-03-10

arxiv.org/abs/math/9803036v4

Mathematics

Algebraic Geometry

Latex, revised version, a much shorter and better written version

Scientific paper

We define relative Gromov-Witten invariants and establish a general gluing theory of pseudo-holomorphic curves for symplectic cutting and contact surgery. Then, we use our general gluing theory to study the change of GW-invariants of Calabi-Yau 3-folds tranform under flops and extremal transitions. We prove a complete formula for the change of GW-invariants of any genus transform under flop and a general type I extremal transition. Other extremal transition will be handled in a subsequent paper.

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