1 M ay 2 00 7 GROMOV - WITTEN THEORY AND NOETHER - LEFSCHETZ THEORY
نویسنده
چکیده
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 to the GromovWitten theory of 1-parameter families ofK3 surfaces. The reduced K3 theory and the Yau-Zaslow formula play an important role. We use results of Borcherds for O(2, 19) lattices and proven mirror transforms to determine the Noether-Lefschetz degrees. In the case of 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. 0. Introduction 0.1. K3 families. Let C be a nonsingular complete curve, and let π : X → C be a 1-parameter family of nonsingular quasi-polarized K3 surfaces. Let L ∈ Pic(X) denote the quasi-polarization of degree ∫
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