Multiple cover formulas for reduced descendent GW invariants on K3 and abelian surfaces are implied by the conjectural families GW/PT correspondence, with the PT side proven via cosections and universality.
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The multiple cover formula for $K3$ and abelian surfaces
Multiple cover formulas for reduced descendent GW invariants on K3 and abelian surfaces are implied by the conjectural families GW/PT correspondence, with the PT side proven via cosections and universality.