- Algebraic Geometry
Ph.D., Mathematics, Brandeis University
My research interests are in Algebraic Geometry and topology of Algebraic Varieties. Recently, my work with Francisco Gallego and Miguel Gonzalez has concentrated on deformation theory of varieties of general type and their moduli spaces, construction of new surfaces of general type with birational canonical map, and classification problems of extremal varieties of general type in all dimensions. Also with Gurjar in recent years, I have worked on topology of algebraic varieties; computing fundamental groups of fibered complex algebraic surfaces of general type with a finite group of automorphisms and its applications. Applications include answering a conjecture of Shafarevich on holomorphic convexity for these families of surfaces with a large moduli, Nori's question on fundamental groups and questions on second homotopy group. I also work on linear series and syzygies of varieties of general type, a passion that can be traced back to my thesis days. Two of my students Jayan Mukerjee and Debaditya Raychaudary have very interesting new results in this topic of syzygies.
- Geometry and topology of varieties of general type
- Degenerations and moduli of algebraic varieties
- Koszul cohomology and syzygies of algebraic varieties