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• W3100418064 abstract "We prove the KKV conjecture expressing Gromov–Witten invariants of $K3$ surfaces in terms of modular forms. Our results apply in every genus and for every curve class. The proof uses the Gromov–Witten/Pairs correspondence for $K3$ -fibered hypersurfaces of dimension 3 to reduce the KKV conjecture to statements about stable pairs on (thickenings of) $K3$ surfaces. Using degeneration arguments and new multiple cover results for stable pairs, we reduce the KKV conjecture further to the known primitive cases. Our results yield a new proof of the full Yau–Zaslow formula, establish new Gromov–Witten multiple cover formulas, and express the fiberwise Gromov–Witten partition functions of $K3$ -fibered 3-folds in terms of explicit modular forms." @default.
• W3100418064 created "2020-11-23" @default.
• W3100418064 creator A5038890583 @default.
• W3100418064 creator A5061805366 @default.
• W3100418064 date "2016-01-01" @default.
• W3100418064 modified "2023-10-18" @default.
• W3100418064 title "THE KATZ–KLEMM–VAFA CONJECTURE FOR SURFACES" @default.
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• W3100418064 doi "https://doi.org/10.1017/fmp.2016.2" @default.
• W3100418064 hasPublicationYear "2016" @default.
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