• R V Gurjar

      Articles written in Proceedings – Mathematical Sciences

    • A tribute to a work of C P Ramanujam

      R V Gurjar

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      In this expository article we describe some recent results on the existence and general properties of complex homology 2-cells and contractible surfaces. The motivation for these can be directly traced back to C P Ramanujam’s important paper, ‘A topological characterization of the affine plane as an algebraic variety’. We also discuss the related results of M Miyanishi, T Sugie and T Fujita.

    • Graded subrings of ℂ[X, Y]

      R V Gurjar

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      We prove the following resultTheorem.Let R be an affine normal 2-dimensional subring of ℂ[X, Y] generated by homogeneous polynomials, say, F1,…,Fn. If the g.c.d. (F1,…,Fn) has at most two distinct linear factors (possibly occurring with multiplicities), then R is isomorphic to a ring of invariants ℂ[v, Y]Wfor some finite group W.

      This generalizes a result of D Anderson on rings generated by monomials. As a corollary of the theorem, we prove some special cases of a conjecture of CTC wall. We also prove some results on general graded affine subrings of ℂ[X, Y].

    • A new proof of Suzuki's formula

      R V Gurjar

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      We give a different proof of a formula of Suzuki and its strengthening by Zaidenberg for the topological Euler characteristic of an affine surface fibered over a curve. We deduce this formula using the ideas for the proof of an analogous formula for a proper morphism.

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