Subject Area: Algebraic Geometry

My research interests include the study of compact and non-compact complex algebraic surfaces and their singularities.

I have investigated cyclic covers of the complex affine plane and completely classified cyclic covers which are ℚ-acyclic, i.e. surfaces with trivial rational homology. One key result in this direction is that all such acyclic surfaces are of logarithmic non-general type and contain at least one affine line.

I have investigated cyclic covers of the
affine plane without any topological condition like acyclicity,
and completely classified those which are not of logarithmic
general type. I am interested in the existence of ℂ^{*}-fibrations on affine surfaces of
logarithmic non-general type, especially those with logarithmic
Kodaira dimension zero. In a joint work with R.V. Gurjar we have
shown that affine surfaces with logarithmic Kodaira dimension
zero and zero canonical divisor, do admit a ℂ^{*}-fibration, except in the case of
complements of smooth cubic curves in ℙ^{2}.

- ℚ-homology planes as cyclic covers of
A
^{2}, J. Math. Soc. Japan. 61 (2009), Vol. 61, No. 2.,. - (with R.V. Gurjar), Cyclic multiple planes of non-general type, preprint.