Complete toric varieties with semisimple automorphism group

Gabriel Barría Galland

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arXiv · 2511.20375

Complete toric varieties with semisimple automorphism group

Gabriel Barría Galland

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Abstract

Let $X$ be a complete toric variety. We give a criterion to decide whether $X$ decomposes as a product of complete toric varieties by analyzing the $1$-skeleton of its fan. More precisely, we prove that any direct-sum decomposition of the 1-skeleton induces a corresponding direct-sum decomposition of the fan itself. As an application, we show that if the identity component of the automorphism group is semisimple, then $X$ must be a product of projective spaces.

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Gabriel Barría Galland. 2025-11-25. Complete toric varieties with semisimple automorphism group. https://arxiv.org/abs/2511.20375

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