arXiv subjects
Publications and source records attributed to Ashwath Rabindranath.
In 1996 as part of the development of arithmetic intersection theory and Arakelov theory, Zhang defined a "GIT height function" for semi-stable algebraic cycles in projective space. In the same work, Zhang conjectured that this height function was positive. We prove this conjecture for zero-cycles and hyperplane arrangements.
We study the nef cones of complex smooth projective surfaces and give a sufficient criterion for them to be non-polyhedral. We use this to show that the nef cone of C x C, where C is a complex smooth projective curve of genus at least 2, is not polyhedral.
We describe a tabulation of (conjecturally) modular elliptic curves over the field Q(sqrt(5)) up to the first curve of rank 2. Using an efficient implementation of an algorithm of Lassina Dembele, we computed tables of Hilbert modular forms of weight (2,2) over Q(sqrt(5)), and via a variety of methods we constructed corresponding elliptic curves, including (again, conjecturally) all elliptic curves over Q(sqrt(5)) that have conductor with norm less than or equal to 1831.