Local Gromov-Witten Invariants are Log Invariants

Abstract

We prove a simple equivalence between the virtual count of rational curves in the total space of an anti-nef line bundle and the virtual count of rational curves maximally tangent to a smooth section of the dual line bundle. We conjecture a generalization to direct sums of line bundles.

15 pages, version accepted for publication in Advances in Mathematics

References in corpus (2)

• Tropical quantum field theory, mirror polyvector fields, and multiplicities of tropical curves
• Curves in Calabi-Yau 3-folds and Topological Quantum Field Theory

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