Timeline for Can monodromy be described by the same matrix for chosen generators in case of the same singularity type?
Current License: CC BY-SA 3.0
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| Nov 4, 2014 at 13:43 | comment | added | Alex Degtyarev | Yes, isotrivial means that. I'm not good at refs. The thing is that, the monodromy group of a non-isotrivial elliptic surface over $\Bbb P^1$ is a subgroup of the modular group of genus zero, hence of finite index, hence non-abelian. I can refer to my book MR2952675, but I'm sure that the statement is much older than that. | |
| Nov 4, 2014 at 0:55 | comment | added | ozheidi | thanks! and isotrivial means nonsingular fibers are isomorphic ? also what is a good reference for this result ? | |
| Nov 3, 2014 at 6:55 | comment | added | Alex Degtyarev | OK, by "typical" I meant simply connected. As it is in your case. But yours is not quite "typical" as its fibers are of type $\tilde A_2^*$. For such a surface, the monodromy group is cyclic if and only if the fibration is isotrivial. | |
| Nov 3, 2014 at 6:44 | comment | added | ozheidi | My example(which is probably an elliptic surface) is where the generic fibers are elliptic curves and singular fibers are (3 of them) three lines intersecting at one point and sorry but why does it have to kill H_1 of the fiber in the elliptic surface case? | |
| Nov 3, 2014 at 6:16 | history | answered | Alex Degtyarev | CC BY-SA 3.0 |