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Let $X$ be a normal, projective algebraic variety. I have a (bad) Weil divisor $D$ and a Cartier divisor $C$. Can it happen that they meet, but in codimension greater than $2$? If yes, does this imply, that their intersection (as a class in $A_{k-2}$) is zero?

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    $\begingroup$ Apply Krull's Hauptidealsatz to $C\cap D$ inside $D$. $\endgroup$ Feb 17, 2014 at 15:11
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    $\begingroup$ OK I see the equation of C cannot cut in D anything of bigger codim and normality has nothing to do with it! Thanks, and sorry for a stupid question. $\endgroup$
    – user27328
    Feb 17, 2014 at 15:22

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