2025/11/25 by Galland, Gabriel Barría
#14J50 #14M25 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2511.20375
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.