Effective cone of a Grassmann bundle over a curve defined over \mathbb F_p

2024/01/15 by Indranil Biswas, Shripad M. Garge, Biswas, Indranil +3
Mathematics · Physics and Astronomy · #11G25 #14G15 #14H60 #Advanced Differential Geometry Research #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2401.07478

openalex publication_date 2024/01/15 · openalex created_date 2024/01/18 · openalex updated_date 2026/07/28

Abstract

Let X be an irreducible smooth projective curve defined over \mathbb F_p and E a vector bundle on X of rank at least two. For any 1 ≤ r < \rm rank(E), let \rm Gr_r(E) be the Grassmann bundle over X parametrizing all the r dimensional quotients of the fibers of E. We prove that the effective cone in \rm NS(\rm Gr_r(E))⊗_{\mathbb Z} \mathbb R coincides with the pseudo-effective cone in \rm NS(\rm Gr_r(E))⊗_{\mathbb Z} \mathbb R. When r = 1 or \rm rank(E)-1, this was proved by A. Moriwaki.

Related

• The effective cone of the space of parametrized rational curves in a Grassmannian
• Slope Semistability and Positive cones of Grassmann bundles
• Effective cones of cycles on products of projective bundles over curves
• The cones of effective cycles on projective bundles over curves
• Seshadri constants and Grassmann bundles over curves