English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We show that the Galois group $Gal(\bar{\Q} /\Q)$ operates faithfully on theset of connected components of the moduli spaces of surfaces of general type,and also that for each element $\sigma \in Gal(\bar{\Q} /\Q)$ different fromthe identity and from complex conjugation, there is a surface of general typesuch that $X$ and the Galois conjugate variety $X^{\sigma}$ have nonisomorphicfundamental groups. The result was announced by the second author at theAlghero Conference 'Topology of algebraic varieties' in september 2006. Beforethe present paper was actually written, we received a very interesting preprintby Robert Easton and Ravi Vakil (\cite{e-v}), where it is proven, with acompletely different type of examples, that the Galois group $Gal(\bar{\Q}/\Q)$ operates faithfully on the set of irreducible components of the modulispaces of surfaces of general type. We also give other simpler examples ofsurfaces with nonisomorphic fundamental groups which are Galois conjugate,hence have isomorphic algebraic fundamental groups.

The absolute Galois group acts faithfully on the connected components of the moduli space of surfaces of general type