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 ℙ2.