Timeline for Problem in Rick Miranda: finding genus of a Projective curve
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Feb 15, 2011 at 3:44 | comment | added | roy smith | I.e. the odd dimensional non singular base locus of a pencil of quadrics of form [A-tB], has always an intermediate Jacobian which is also the Jacobian of a hyperelliptic curve, defined as the double cover of the P^1 parametrizing the pencil, and branched over the singular quadrics in the pencil, i.e. the zeroes of det[A-tB]. as I recall. Perhaps this is due to Weil as well. Going to the base locus of three quadrics in P^2g, we get a base locus whose intermediate Jacobian is the Prym variety of the associated double cover of the curve of singular quadrics in the net. as memory serves. | |
| Feb 14, 2011 at 23:47 | comment | added | roy smith | There is nothing trivial about it. And if you do the same thing in P^5, you get a hyperelliptic curve whose jacobian is isomorphic to the intermediate jacobian of the threefold base locus of that pencil of quadrics. Now you are already at the level of a PhD thesis of the 1970's. | |
| Feb 14, 2011 at 0:41 | comment | added | Qiaochu Yuan | @Felipe: actually it was at RSI (cee.org/programs/rsi). Thank you for the reference! I have always wondered just how trivial my paper was... | |
| Feb 14, 2011 at 0:22 | comment | added | Felipe Voloch | This is classical. It is, e.g. in Weil's book "Number Theory: an approach to history" pg 136. Still, that's some high school you went to! | |
| Feb 13, 2011 at 23:38 | history | answered | Qiaochu Yuan | CC BY-SA 2.5 |