Noether-Lefschetz locus in enumerative geometry. - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T01:26:04Z http://mathoverflow.net/feeds/question/14732 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/14732/noether-lefschetz-locus-in-enumerative-geometry Noether-Lefschetz locus in enumerative geometry. Csar Lozano Huerta 2010-02-09T03:23:38Z 2010-02-09T14:59:12Z <p>It is well known that if you have a smooth quartic surface $X\subset \mathbb{P}^3$, it may or may not have lines in it. Indeed, $X$ has the following options, 64 (the maximal number), 32, 16, or none.</p> <p>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.</p> <p>Is all the enumerative information about such quartics encoded in $D$?</p> <p>I'd like to know more about such a divisor $D$. So, Could someone recommend free-references of this online?</p>