Torus embedding and fiber space

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In the research, the following four objects related to the theories of torus embedding and torus fibration were studied :1. Toric bundles; 2. Nearly smooth torus fibrations; 3. Varieties admitting non-trivial surjective endomorphisms; 4. Normal quartic surfaces and log del Pezzo surfaces.1. Constructions of toric bundles and description of divisors on them are given. Unfortunately, there was no significant progress toward constructing the theory of degenerations of tonic bundles.2. The local structure of a Kahler torus fibration is determined when the singular fibers have open neighborhoods whose universal covering space does not have any positive dimensional subvarieties. The global bimeromorphic equivalence classes of Kahler torus fibrations which have locally finite monodromies are described as elements of a certain cohomology group under a fixed variation of Hodge structure.3. By the theories of torus embedding and elliptic fibration, the classification of varieties admitting non-trivial surjective endomorphisms is done in the cases of nonsingular compact complex surfaces and nonsingular projective threefolds with non-negative Kodaira dimension (joint work with Yoshio Fujimoto).4. The classification of normal quartic surfaces with irrational singularities (joint work with Yuji Ishii) and that of log del Pezzo surfaces of index two are given by the ideas of separation of divisors and the elimination of a zero-dimensional subscheme, respectively.