Alok Maharana

PIC

Subject Area: Algebraic Geometry

Background and Research Interests

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 -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 *-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 *-fibration, except in the case of complements of smooth cubic curves in 2.

Select Publications

  1. -homology planes as cyclic covers of A2, J. Math. Soc. Japan. 61 (2009), Vol. 61, No. 2.,.
  2. (with R.V. Gurjar), Cyclic multiple planes of non-general type, preprint.