Articles written in Proceedings – Mathematical Sciences

    • Classification of isolated complete intersection singularities

      A J Parameswaran

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      In this article we prove that an isolated complete intersection singularity (V,0) is characterized by a module of finite lengthA(V) (cf. §1 for definition) associated to it. The proof uses the theory of finitely determined map germs and generalises the corresponding result by Yau and Mather [4], for hypersurfaces.

    • Character on a homogeneous space


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      In this paper, we look at the notion of cohomological triviality of fibrations of homogeneous spaces of affine algebraic groups defined over $\mathbb{C}$ and use topological methods, primarily the theory of covering spaces. This is made possible because of the structure theory of affine algebraic groups. Further, we generalize our results for arbitrary connected algebraic groups and their homogeneous spaces. As an application of our methods, we give a structure result for quasi- reductive algebraic groups (i.e., algebraic groups whose unipotent radical is trivial), up to isogeny.

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