Etale endomorphisms of algebraic varieties

1.首席投资人与K.Masuda合作，研究了允许G_m作用的代数曲面的自同态，证明了它们几乎在所有情况下都是自同构。另一方面，他考虑了具有有限群作用的代数曲面的分类，并表明我们可以在没有群作用的情况下提出平行论点，但需要更微妙的论点。此外，他和K.Masuda考虑了允许两个代数独立的G_a作用的q-同调平面，并证明了它们的泛覆盖是由xy=z^2-1.2定义的超曲面。Fujiki考虑了射影平面及其相关的扭曲空间(三维复流形)的(可微)连通和MP^2的自对偶度量，并观察到扭曲空间在各种度量下可取的代数维数的最大值。他在相关主题上得到了许多结果。3.T.Hibi考虑了与根系统和完全二部图有关的组态的正规化体积所对应的Toric理想的Groebner基。他得到了许多关于计算代数的结果。4.S.Usui与K.Kato合作，通过考虑对称空间Γ\D的环面紧化实现了所谓的Griffith梦想，当D具有极化Hodge结构时。

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.