On pseudo-effective cones of projective bundles and volume function

Abstract

In this paper, we compute the pseudo-effective cones of various projective bundles 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 fiber product (E) ×C(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. © 2025 World Scientific Publishing Company.