Counting Elliptic Curves in K3 Surfaces
classification
🧮 math.SG
math.AGmath.DG
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formulaclassesgenusnon-primitivesurfacesapproachcalculationscompute
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We compute the genus one family Gromov-Witten invariants of K3 surfaces for non-primitive classes. These calculations verify Gottsche-Yau-Zaslow formula for non-primitive classes with index two. Our approach is to use the genus two topological recursion formula and the symplectic sum formula to establish relationships among various generating functions.
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