2014/08/08 by Stephen Kudla, Kudla, Stephen
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT
paper · pdf · doi:10.48550/arxiv.1408.1907
This article appeared in Arithmetic and Geometry of K3 Surfaces and Calabi-Yau Threefolds, Laza, Scheutt and Yui, eds. Fields Institute Comm. 67, 2013
arxiv created 2014/08/08 · arxiv updated 2014/08/11
We describe the application of the results of Kudla-Millson on the modularity of generating series for cohomology classes of special cycles to the case of lattice polarized K3 surfaces. In this case, the special cycles can be interpreted as higher Noether-Lefschetz loci. These generating series can be paired with the cohomology classes of complete subvarieties of the moduli space to give classical Siegel modular forms with higher Noether-Lefschetz numbers as Fourier coefficients. Examples of such complete families associated to quadratic spaces over totally real number fields are constructed. A more explicit and concrete construction of such families and the resulting modular forms would be of interest.