Seshadri constants and Grassmann bundles over curves

2018/03/23 by Biswas, Indranil, Hanumanthu, Krishna, Nagaraj, D. S. +1
#14C20 #14H60 #14Q20 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1803.08648

Abstract

Let X be a smooth complex projective curve, and let E be a vector bundle on X which is not semistable. For a suitably chosen integer r, let Gr(E) be the Grassmann bundle over X that parametrizes the quotients of the fibers of E of dimension r. Assuming some numerical conditions on the Harder-Narasimhan filtration of E, we study Seshadri constants of ample line bundles on Gr(E). In many cases, we give the precise value of Seshadri constant. Our results generalize various known results for \rm rank(E)=2.

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