Let $X \to Y$ be a morphism of schemes. Let $ D \subset X$ be a closed subscheme. $D$ is called a relative effective Cartier divisor if $D$ is effective and $D \to Y$ is flat.
What is the "relative degree" of a (Cartier) divisor? How is it defined?
This terminology I found in "Higher Genus Curves in Mathematical Physics and Arithmetic Geometry" (by Andreas Malmendier, Tony Shaska) page 217. it used also in "Twelve points on the projective line, branched covers, and rational elliptic fibrations" by Ravi Vakil.