Timeline for The locus of rational/elliptic curves on a special surface in $\mathbb{P}^3$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Sep 11, 2014 at 10:33 | comment | added | mehdi | this locus is not explicitly computed in the Voisin's paper | |
| Sep 11, 2014 at 10:06 | comment | added | Remke Kloosterman | No, because all your hypersurface may be contained in the locus where the conclusion of Voisin's result does not hold. | |
| Sep 10, 2014 at 18:41 | comment | added | mehdi | Dear Remke, According to the above paper by Voisin every general hypersurface in $P^n$ of degree $d\ge 2n-1$ contains no rational curve. In my case the polynomials P and Q can be taken general (e.g. their coefficients are general) can I deduce that by Voisin theorem the above hypersurface for $d\ge 5$ contains no rational curve? | |
| Sep 9, 2014 at 13:17 | comment | added | Remke Kloosterman | Voisin's paper concerns varieties of general type, Ulmer's preprint is partly an extension of Voisin's strategy to hypersurfaces of degree 6k in P(1,1,2k,3k), and for your problem it would be probably sufficient to extend Voisin's method to the family of hypersurfaces of degree 2d in Ps(1,1,1,d) with d^2 nodes. | |
| Sep 9, 2014 at 7:36 | comment | added | mehdi | May be it works, but note that these surfaces are not K3 surfaces or elliptic surfaces (like in Ulmer's paper . In fact they are general type surfaces. | |
| Sep 8, 2014 at 20:34 | history | answered | Remke Kloosterman | CC BY-SA 3.0 |