Noether-Lefschetz theory and the Yau-Zaslow conjecture

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dc.creatorKlemm, A.
dc.creatorMaulik, D.
dc.creatorPandharipande, R.
dc.creatorScheidegger, E.
dc.date2008-07-15
dc.date2008-12-28
dc.date.accessioned2026-07-07T12:22:08Z
dc.date.available2026-07-07T12:22:08Z
dc.descriptionThe Yau-Zaslow conjecture determines the reduced genus 0 Gromov-Witten invariants of K3 surfaces in terms of the Dedekind eta function. Classical intersections of curves in the moduli of K3 surfaces with Noether-Lefschetz divisors are related to 3-fold Gromov-Witten theory via the K3 invariants. Results by Borcherds and Kudla-Millson determine the classical intersections in terms of vector-valued modular forms. Proven mirror transformations can often be used to calculate the 3-fold invariants which arise. Via a detailed study of the STU model (determining special curves in the moduli of K3 surfaces), we prove the Yau-Zaslow conjecture for all curve classes on K3 surfaces. Two modular form identities are required. The first, the Klemm-Lerche-Mayr identity relating hypergeometric series to modular forms after mirror transformation, is proven here. The second, the Harvey-Moore identity, is proven by D. Zagier and presented in the paper.
dc.description40 pages
dc.identifierhttps://arxiv.org/abs/0807.2477
dc.identifierhttp://arxiv.org/abs/0807.2477
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/213552
dc.subjectAlgebraic Geometry
dc.subjectHigh Energy Physics - Theory
dc.subjectSymplectic Geometry
dc.titleNoether-Lefschetz theory and the Yau-Zaslow conjecture
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