Timeline for A K3 over $P^1$ with six singular $A_1$- fibers?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Oct 1, 2011 at 1:30 | vote | accept | Richard Montgomery | ||
| Sep 26, 2011 at 4:00 | vote | accept | Richard Montgomery | ||
| Oct 1, 2011 at 1:30 | |||||
| Sep 26, 2011 at 3:56 | comment | added | Richard Montgomery |
Yes! That is our base! We, Rick Moeckel and I, arrive at it by starting with the the planar 4 body problem of celestial mechanics. Quotient by translations and rotations. Levi-Civita'' regularize the binary collisions. Result:the phase space is the cotangent bundle of the cone of Hirzebruch's surface BEFORE regularizing the 4 points. Do the same for 3 bodies. Result: the cotangent bundle of the cone over Noam's $a^2 + b^2 + c^2 =0$ conic. Fibration: forget one of the bodies''.
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| Sep 25, 2011 at 19:52 | comment | added | Noam D. Elkies | ...and the base is then the conic $a^2+b^2+c^2=0$, with the octahedral symmetry given by the signed permutation group, and the six vertices of the octahedron at $abc=0$. | |
| Sep 25, 2011 at 16:48 | history | edited | Noam D. Elkies | CC BY-SA 3.0 |
Added identification with universal curve over X(4), likely answering OP's first question "do you know this second K3?"
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| Sep 25, 2011 at 3:13 | history | answered | Noam D. Elkies | CC BY-SA 3.0 |