An example on volumes jumping over Zariski dense set

TL;DR

This paper presents an example demonstrating that the volume of an -divisor on a family of complex smooth surfaces can jump infinitely often over prime divisors in the base, illustrating complex behavior in algebraic geometry.

Contribution

It provides a concrete example of volume jumping behavior over infinitely many prime divisors, extending previous constructions in algebraic geometry.

Findings

Volume of -divisors jumps infinitely often

Behavior occurs over prime divisors in the base

Builds on existing construction methods

Abstract

We give an example that the volume of an $\mathbb{R}$-divisor on a family of complex smooth surfaces jumps at infinite many prime divisors in the base. Our example follows the construction in \cite{1}.