Hodge Index Theorem and the Adjunction Formula
In a fundamental paper [Ara 2], Arakelov showed how to complete a family of curves over the ring of integers of a number field by introducing the components at infinity, and getting a divisor class group which in many ways plays the role of the Picard group on complete surfaces.
KeywordsLine Sheaf Residue Theorem Canonical Sheaf Cartier Divisor Horizontal Curve
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