Communications in Analysis and Geometry

Volume 14 (2006)

Number 1

Counting Curves in Elliptic Surfaces by Symplectic Methods

Pages: 107 – 134

DOI: http://dx.doi.org/10.4310/CAG.2006.v14.n1.a5

Author

Junho Lee

Abstract

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.

Full Text (PDF format)