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Combinatorial descriptions of toric extremal contractions
Hiroshi Sato
In this paper, we give explicit combinatorial descriptions for toric extremal contractions under the relative setting, where varieties do not need to be complete. Fujino's completi…
Wild hypersurface bundles over toric varieties
Hiroshi Sato
In this paper, we investigate when there exists a wild hypersurface bundle over a smooth proper toric variety in positive characteristic. In particular, we determine the possibilit…
Toric Fano varieties with divisorial contractions to curves
Hiroshi Sato
In this paper, we obtain a complete classification of smooth toric Fano varieties equipped with extremal contractions which contract divisors to curves for any dimension. As an app…
Jumping deformations of complete toric varieties
Hiroshi Sato
We construct one-parameter complex analytic families whose special fibers are complete toric varieties. Under some assumptions, the general fibers of these families also become tor…
The classification of smooth toric weakened Fano 3-folds
Hiroshi Sato
We completely classify toric weakened Fano 3-folds, that is, smooth toric weak Fano 3-folds which are not Fano but are deformed to smooth Fano 3-folds. There exist exactly 15 toric…
Remarks on abelian surfaces in nonsingular toric Fano 4-folds
Hiroshi Sato
In this paper, we investigate whether the 124 nonsingular toric Fano 4-folds admit totally nondegenerate embeddings from abelian surfaces or not. As a result, we determine the poss…