Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

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- Talk [1]

Date:

Wed, 2018-05-30 14:30 - 15:30 Given two semistable elliptic surfaces over a smooth, projective curve $C$ defined over a field of characteristic zero or finitely generated over its prime field, we show that any compatible family of effective isometries of the N{\'e}ron-Severi lattices of the base changed elliptic surfaces for all finite separable maps $B\to C$ arises from

an isomorphism of the elliptic surfaces. Without the effectivity hypothesis, we show that the two elliptic surfaces are isomorphic.

We also determine the group of universal automorphisms of a semistable elliptic surface. In particular, this includes showing that the Picard-Lefschetz transformations corresponding to an irreducible component of a singular fibre, can be extended as universal isometries. In the process, we get a family of homomorphisms of the affine Weyl group associated to $\tilde{A}_{n-1}$ to that of $\tilde{A}_{dn-1}$, indexed by natural numbers $d$, which are closed under composition.

This is joint work with S. Subramanian.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/158