Let $X$ be a smooth projective variety of dimension $3$, and $L$ an ample line bundle with $h^0(X,L)\geq 2$. Let $s$ and $t$ be two generic linearly independent sections of $L$, and $C$ the curve that they define.
Assume we know all intersection numbers $L^3$, $L^2K_X$, $LK_X^2$ and $K_X^3$.
Of course we can compute the genus of $C$ by adjunction. Assume now that $C$ is irreducible but non-reduced, and of multiplicity $2$. In this case, we can also compute the genus of $C_{red}$ by adjunction: restricting $L$ to $\{s=0\}$ we get $2H$ for some line bundle $H$, and $C_{red}$ is defined by a section of $H$.
Now, take different sections and assume that the curve $C'$ you get has two irreducible components, say $A$ and $B$, with $A$ reduced and $B$ non-redued of multiplicity two.
Can I say something about the genus of $B_{red}$? For instance, is it smaller than the genus of $C_{red}$ computed in the previous paragraph?