On the local isomorphism property for families of K3 surfaces

TL;DR

This paper constructs examples of K3 surface families that are pointwise identical but not locally isomorphic, providing a negative answer to a longstanding question and challenging recent assumptions.

Contribution

It presents explicit counterexamples of K3 surface families that are pointwise isomorphic but not locally isomorphic, addressing a question from 1977.

Findings

Counterexamples to local isomorphism property for K3 families

Challenges previous assumptions in the field

Provides new insights into K3 surface family structures

Abstract

We construct two families of K3 surfaces over a complex manifold $S$ such that the families are pointwise isomorphic but not locally isomorphic over $S$. This answers a question of Wehler from 1977 in the negative and challenges a more recent result of Meersseman.