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arXiv · 1702.08808

Finiteness of real structures on KLT Calabi-Yau regular smooth pairs of dimension 2

Mohamed Benzerga
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Abstract

In this article, we prove that a smooth projective complex surface $X$ which is regular (i.e. such that $h^1(X,\mathcal O_X)=0$) and which has a $\mathbb{R}$-divisor $\Delta$ such that $(X,\Delta)$ is a KLT Calabi-Yau pair has finitely many real forms up to isomorphism. For this purpose, we construct a complete CAT(0) metric space on which $\text{Aut }X$ acts properly discontinuously and cocompactly by isometries, using Totaro's Cone Theorem. Then we give an example of a smooth rational surface with finitely many real forms but having a so large automorphism group that our previous result (see https://arxiv.org/abs/1409.3490) does not predict this finiteness.

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Mohamed Benzerga. 2017-02-28. Finiteness of real structures on KLT Calabi-Yau regular smooth pairs of dimension 2. https://arxiv.org/abs/1702.08808

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