Relative forms of real algebraic varieties and examples of quasi-projective surfaces with algebraic moduli of real forms

2022/06/03 by Bot, Anna, Dubouloz, Adrien
#14J26 #14J50 #14P25 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.01713

Abstract

We propose a framework to give a precise meaning to the intuitive notion of "family of real forms of a variety parametrised by a variety" and study some fundamental properties of this notion. As an illustration, for any n ≥ 1, we construct the first example of a quasi-projective real surface whose mutually non-isomorphic real forms admit a moduli of dimension at least n, parametrised by the real points of an affine n-space. Expanding on these constructions, we can give quasi-projective real varieties of any dimension whose algebraic moduli of the non-isomorphic real forms has arbitrarily positive dimension.

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