# 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.

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