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The main motivation of this paper arises from classical questions about actions of Lie groups preserving a geometric structure: which Lie groups can act on a manifold preserving a given structure, a...
We prove that the automorphism group of an odd dimensional Calabi-Yau manifold of Picard number two is always a finite group. This makes a sharp contrast to the automorphism groups of K3 surfaces and ...
Let G be a connected reductive complex algebraic group acting on a smooth complete complex algebraic variety X. We assume that X under the action of G is a regular embedding, a condition satisfied in ...
Abstract: We prove that the birational automorphism group of any Calabi-Yau manifold given by a generic hypersurface of multi-degree two in $({\mathbf P^1})^{n+1}$ is isomorphic to the universal Coxet...
We prove that the automorphism group of the dihedral quandle with n elements is isomorphic to the affine group of the integers mod n, and also obtain the inner automorphism group of this quandle. In...
We obtain analogues of classical results on automorphism groups of holomorphic fiber bundles, in the setting of group schemes. Also, we establish a lifting property of the connected automorphism group...
Let G be a free group in a variety of groups, but G is not absolutely free. We prove that the group of automorphisms Aut(G) is linear if and only if G is a finitely generated virtually nilpotent group...
Let G be a free group in a variety of groups, but G is not absolutely free. We prove that the group of automorphisms Aut(G) is linear if and only if G is a finitely generated virtually nilpotent group...
A compact Riemann surface X of genus g is called an (M-1)-surface if it admits an anticonformal involution that fixes g simple closed curves, the second maximum number by Harnack's theorem. If X also ...

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