Etale endomorphisms of algebraic varieties

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1.Head investingator, in collaboration with K.Masuda, considered etale endomorphisms of algebraic surfacees admitting G_m-actions and showed that they are automorphisms almost in all cases. On the other hand, he considered a classification of algebraic surfacees with finite group actions arid showed that we can make parallel arguments with the case without group actions but need more subtle arguments. Furthermore, he with K. Masuda considered Q-homology planes admitting two algebraically independent G_a-actions and showed that their universal coverings are hypersurfaces defined by xy=z^2-1.2.A.Fujiki considered self-dual metrics for a(differentiable) connected sum mP^2 of the projective plane and associated twister spaces(3-dimensional complex manifolds) and observed maximal value of algebraic dimension which twister spaces can take for various metrics. He obtained many results on the related topics.3.T.Hibi considered the Groebner basis of the toric ideal associated with the normalized volumes of configurations related with root systems and complete bipartite graphs. He obtained many results on computational algebras.4.S.Usui, in collaboration with K.Kato, realized a so-called Griffith's dream by considering the toroidal compactification of a symmetric space Γ＼D, when D has polarized Hodge structures.5.Y.Shinohara considered the generalized pretzel links and computed the associated Jones polynomials.