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arXiv · 2206.01713

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

Anna Bot·Adrien Dubouloz
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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 $n \geq 1$, 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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Anna Bot, Adrien Dubouloz. 2022-06-03. Relative forms of real algebraic varieties and examples of quasi-projective surfaces with algebraic moduli of real forms. https://arxiv.org/abs/2206.01713

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