Slope Semistability and Positive cones of Grassmann bundles

2022/05/23 by Misra, Snehajit, Ray, Nabanita
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2205.11289

Abstract

Let E be a vector bundle of rank r on a smooth complex projective variety X. In this article, we compute the nef and pseudoeffective cones of divisors in the Grassmann bundle Gr_X(k,E) parametrizing k-dimensional subspaces of the fibers of E, where 1≤ k ≤ rank(E), under assumptions on X as well as on the vector bundle E. In particular, we show that nef cone and the pseudoeffective cone of Gr_X(k,E) coincide if and only if E is a slope semistable bundle on X with c₂(End(E))=0. We also discuss about the nefness and ampleness of the universal quotient bundle Q_k on Gr_X(k,E).

Related

• Effective cone of a Grassmann bundle over a curve defined over \mathbb F_p
• CM-line bundles and slope \K-semistability for big and nef line bundles along subschemes
• Slope semistability of rank 2 Lazarsfeld-Mukai bundles on K3 surfaces and ACM line bundles
• Nef cone and Seshadri constants on products of projective bundles over\n curves
• Seshadri constants and Grassmann bundles over curves