H. Ananthnarayan

Research Interests

Math Arxiv



   My main interests lie in commutative algebra, the study of commutative rings and modules over them. I am currently working on understanding a new construction of Gorenstein rings called the connected sum. I am also studying various aspects of fibre products of rings and establishing connections of fibre products with connectedness theorems and exploring their links to the theory of Gorenstein liaison.
   In my earlier work, one project involved approximating Artinian rings by Gorenstein rings using the notion of Gorenstein colength. Part of the work dealt with studying bounds on this number and the other involved constructing Gorenstein Artin rings. Techniques used include studying inverse systems, maps from the injective hull of the residue field to the ring, the Hoskin-Deligne formula, the strong Lefschetz property and fiber products and connected sums of Gorenstein Artin local rings.

  Another problem I have worked on dealt with multiplicities and minimal reductions of the maximal ideal in a local ring. P
art of the work was to understand when the maximal ideal is 3-standard, using tools from the world of positive characteristic and applying the technique of reducing to prime characteristic.

§ Research Summary

§ Publications

6. Homological and Connectedness Properties of Fibre Products
(with E. Celikbas and Z. Yang)
Work in Progress
5. Linking Constructions of Gorenstein Rings Work in Progress

4. Connected Sums of Gorenstein Rings
(with Luchezar L. Avramov and W. Frank Moore)

Crelle J, to appear.

3. Three-Standardness of the Maximal Ideal
(with C. Huneke)
Journal of Pure and Applied Algebra, vol. 215, no. 11, (2011) 2674-2683.
2. Computing Gorenstein Colength
Journal of Commutative Algebra, vol. 1, no. 3, (2009) 343-359.
1. The Gorenstein Colength of an Artinian Local Ring
Journal of Algebra 302 (2008) 3438-3446.

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