# Journal of the Ramanujan Mathematical Society

Volume 35, Issue 4, December 2020  pp. 317–325.

Nef cone and Seshadri constants on products of projective bundles over curves

Authors:  Rupam Karmakar and Snehajit Misra
Author institution:Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600~113, India and Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400~094, India

Summary:  Let X = P(E{1}) ×{C} P (E{2}) where C is a smooth curve and let E{1}, E{2} be vector bundles over C. In this paper, we extend the results in [KMR] by computing the nef cone of X without restriction on the rank or semistability~of E{1} and E{2}. We also study the Seshadri constants of ample line bundles on X. We calculate the Seshadri constants in some cases and give bounds in some of the remaining cases.