Noether-Lefschetz locus in enumerative geometry.

It is well known that if you have a smooth quartic surface $Xsubset mathbb{P}^3$, it may or may not have lines in it. Indeed, $X$ has the following options, 64 (the maximal number), 32, 16, or none.

Between the space of all such quartics in $mathbb{P}^3$ which is $|mathcal{O}_{mathbb{P}^3}(4)|=mathbb{P}^{34}$, those with at least one line in it form a divisor $D$. Therefore, intersections of such a divisor with curves in $mathbb{P}^{34}$ may give enumerative information about points(quartics) in the intersection.

Is all the enumerative information about such quartics encoded in $D$?

I'd like to know more about such a divisor $D$. So, Could someone recommend free-references of this online?

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