In this paper,we explicitly compute the Kodaira-Spencer map over a quaternionic Shimura curve over the field of rational numbers,and also compute its effect on the metrics of the Hodge bundle.The former is based on moduli interpretation and deformation theory,and the latter is based on the theory of complex abelian varieties.
Shimura curveKodaira-Spencer mapHodge bundleintegral modelmoduli space
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