A remark on the Ueno-Campana's threefold

TL;DR

This paper proves that the Ueno-Campana's threefold cannot be constructed by blowing up a smooth threefold along a smooth center, resolving a previously open question in algebraic geometry.

Contribution

It provides a negative answer to whether the Ueno-Campana's threefold can be obtained via a blow-up along a smooth center, clarifying its geometric structure.

Findings

Ueno-Campana's threefold cannot be obtained as a blow-up of any smooth threefold.

Answers a question posed by Oguiso and Truong.

Advances understanding of the geometric properties of special threefolds.

Abstract

We show that the Ueno-Campana's threefold cannot be obtained as the blow-up of any smooth threefold along a smooth centre, answering negatively a question raised by Oguiso and Truong.