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math.AG2026
On the gap between the integral and rational Gongyo indices of toric Fano varieties
Hiroshi Sato
Exact calculations for smooth toric Fano varieties in dimensions at most seven suggest a sharp dimension-dependent lower bound for the positive difference between the rational and…
math.AG2026
An affine local criterion for toric projective space bundles
Osamu Fujino, Hiroshi Sato
We study when an equidimensional toric morphism is forced to be a projective-space bundle. Our main result is an affine rigidity theorem: if the base space is affine, the toric rel…
math.AG2026
Non-projective complete log canonical surfaces
Osamu Fujino, Nao Moriyama, Hiroshi Sato
We construct non-projective complete log canonical algebraic surfaces whose canonical divisor is semi-ample over any algebraically closed field other than the algebraic closure of…