On pseudoeffective cones of projective bundles and volume function

2022/03/14 by Misra, Snehajit, Singh, Anoop
#14D06 #14E30 #14E99 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14C20 #Secondary 14D20

paper · doi:10.48550/arxiv.2203.07007

Abstract

In this article, we compute the pseudo-effective cones of various projective bundles ℙ_X(E) over higher dimensional varieties X under some assumptions on X as well as on the vector bundle E. We also compute the volume function on fibre product ℙ(E)×_Cℙ(F) of two projective bundles over a smooth irreducible complex projective curve C. In particular, we show that the volume function on the fiber product of two ruled surfaces is of polynomial type.

Related

• Characterizing volume via cone duality
• Effective cones of cycles on products of projective bundles over curves
• The cones of effective cycles on projective bundles over curves
• Volume of Perturbations of Pseudoeffective Classes
• Smooth projective surfaces with pseudo-effective tangent bundles