Counting Curves in Elliptic Surfaces by Symplectic Methods

We explicitly compute family GW invariants of elliptic surfaces for primitive classes. That involves establishing a TRR formula and a symplectic sum formula for elliptic surfaces and then determining the GW invariants using an argument from [9]. In particular, as in [2], these calculations also confirm the well-known Yau–Zaslow Conjecture [22] for primitive classes in $K3$ surfaces.

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Published 1 January 2006