Modularity of Equations D3 and the Iskovskikh Classification
نویسنده
چکیده
We study conditions for a d –Kummer pullback of a Picard–Fuchs equation in a twisted symmetric square of the universal elliptic curve over X0(N) W to be of type D3. Our main result says that the only possible pairs (N, d) are exactly those for which there exists a Fano threefold with one-dimensional Picard group whose index is d and whose anticanonical degree is 2d2N. We give some modular formulas for each of these 17 cases, and conclude with a conjecture on counting numbers for the corresponding Fano threefolds.
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