An example of non-homeomorphic conjugate varieties

TL;DR

This paper provides examples of complex algebraic varieties that are not topologically equivalent to their conjugates, highlighting subtle differences in the topology of conjugate varieties within the context of Shimura varieties.

Contribution

It presents the first known examples of non-homeomorphic conjugate varieties in the setting of connected Shimura varieties.

Findings

Examples of non-homeomorphic conjugate varieties are constructed.

Conjugate varieties can have different topological types in the context of Shimura varieties.

Abstract

We give examples of smooth quasi-projective varieties over complex numbers, in the context of connected Shimura varieties, which are not homeomorphic to a conjugate of itself by an automorphism of the complex numbers.