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Explicit Bicanonical Models of Eight Fake Quadrics · arXivDesk

2608.12296Aug 12, 2026

Explicit Bicanonical Models of Eight Fake Quadrics

Lev Borisov, Carlos Rito

Abstract

We compute explicit defining equations for eight fake quadrics arising as $\mathbb Z/2\times\mathbb Z/4$ -covers of two singular $\mathbb Z/2$ -Godeaux surfaces obtained in earlier work of the second author. Starting from explicit equations for the universal covers of the Godeaux surfaces, we reconstruct the relevant character eigenspaces and determine the homogeneous ideals of the bicanonical models of the eight fake quadrics in $\mathbb P^8$ . All eight models are defined over $\mathbb Q$

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We compute explicit defining equations for eight fake quadrics arising as Z/2× Z/4-covers of two singular Z/2-Godeaux surfaces obtained in earlier work of the second author. Starting from explicit equations for the universal covers of the Godeaux surfaces, we reconstruct the relevant character eigenspaces and determine the homogeneous ideals of the bicanonical models of the eight fake quadrics in P⁸.

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The paper addresses: Explicit Bicanonical Models of Eight Fake Quadrics.
We compute explicit defining equations for eight fake quadrics arising as Z/2× Z/4-covers of two singular Z/2-Godeaux surfaces obtained in earlier work of the second author.