Timeline for A K3 over $P^1$ with six singular $A_1$- fibers?

6 events

when toggle format	what		by	license	comment
Oct 1, 2011 at 6:52	history	edited	rita	CC BY-SA 3.0	added 108 characters in body
Oct 1, 2011 at 6:49	comment	added	rita		In fact, I had made a mistake: the preimage of the line $P_1P_i$ is the disjoint union of 2 $I_4$ fibers. Thanks for pointing this out. I'm going to edit my answer.
Oct 1, 2011 at 0:48	comment	added	Richard Montgomery		If $f: X \to C$ is an elliptic fibration over a curve $C$, then this formula: $\chi(X) = \sum_{s\in T} e(F_s)$, from Barth et al that Rita referenced has been wonderfully helpful. If the symmetry group of $X$ is fiber-preserving and permutes the singular fibers, as in my case, that formula becomes $24 = n e(F)$ where $n$ is the number of these singular fibers. For me $n = 6$ so $e(F) = 4$. This `$4$' is the same` 4' of the 4 spheres ($P^1$'s) making Noam Elkie's $I_4$.
Sep 25, 2011 at 16:51	history	edited	rita	CC BY-SA 3.0	added 124 characters in body
Sep 25, 2011 at 16:14	history	edited	rita	CC BY-SA 3.0	deleted 16 characters in body
Sep 25, 2011 at 15:49	history	answered	rita	CC BY-SA 3.0