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摘要翻译：
K3曲面模中的Noether-Lefschetz因子是Picard秩至少为2的轨迹。我们将K3曲面的1-参数族中的Noether-Lefschetz因子的次数与3重全空间的Gromov-Witten理论联系起来。约化K3理论和Yau-Zaslow公式起着重要作用。利用O(2,19）格的Borcherds和Kudla-Millson的结果，确定了经典K3曲面族中2,4,6和8度的Noether-Lefschetz度。对于四次K3曲面，证明了Noether-Lefschetz度是权重为21/2和水平为8的显式模形式的Fourier系数。讨论了与镜像对称的相互作用。我们以关于K3曲面模空间的Picard秩的一个猜想结束。
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英文标题：
《Gromov-Witten theory and Noether-Lefschetz theory》
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作者：
D. Maulik and R. Pandharipande
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最新提交年份：
2012
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
Noether-Lefschetz divisors in the moduli of K3 surfaces are the loci corresponding to Picard rank at least 2. We relate the degrees of the Noether-Lefschetz divisors in 1-parameter families of K3 surfaces to the Gromov-Witten theory of the 3-fold total space. The reduced K3 theory and the Yau-Zaslow formula play an important role. We use results of Borcherds and Kudla-Millson for O(2,19) lattices to determine the Noether-Lefschetz degrees in classical families of K3 surfaces of degrees 2, 4, 6 and 8. For the quartic K3 surfaces, the Noether-Lefschetz degrees are proven to be the Fourier coefficients of an explicitly computed modular form of weight 21/2 and level 8. The interplay with mirror symmetry is discussed. We close with a conjecture on the Picard ranks of moduli spaces of K3 surfaces.
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PDF链接：
https://arxiv.org/pdf/0705.1653
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