Curve counting on K3 × E, the Igusa Cusp form χ10, and descendent integration
Let S be a nonsingular projective K3 surface. Motivated by the study of the Gromov-Witten theory of the Hilbert scheme of points of S, we conjecture a formula for the Gromov-Witten theory (in all curve classes) of the Calabi-Yau 3-fold S × E where E is an elliptic curve. In the primitive case, our c...
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| Main Authors: | , |
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| Format: | Chapter/Article |
| Language: | English |
| Published: |
2016
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| In: |
K3 surfaces and their moduli
Year: 2016, Pages: 245-278 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://link.springer.com/chapter/10.1007/978-3-319-29959-4_10
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| Author Notes: | G. Oberdieck and R. Pandharipande |
MARC
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| 520 | |a Let S be a nonsingular projective K3 surface. Motivated by the study of the Gromov-Witten theory of the Hilbert scheme of points of S, we conjecture a formula for the Gromov-Witten theory (in all curve classes) of the Calabi-Yau 3-fold S × E where E is an elliptic curve. In the primitive case, our conjecture is expressed in terms of the Igusa cusp form χ10 and matches a prediction via heterotic duality by Katz, Klemm, and Vafa. In imprimitive cases, our conjecture suggests a new structure for the complete theory of descendent integration for K3 surfaces. Via the Gromov-Witten/Pairs correspondence, a conjecture for the reduced stable pairs theory of S × E is also presented. Speculations about the motivic stable pairs theory of S × E are made. The reduced Gromov-Witten theory of the Hilbert scheme of points of S is much richer than S × E. The 2-point function of Hilbd(S) determines a matrix with trace equal to the partition function of S × E. A conjectural form for the full matrix is given. | ||
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