Minzhe Zhu

2003 Guanghua East Tower

220 Handan Road

Shanghai, Yangpu

Hi! I am a Ph. D. student in School of Mathematical Sciences, Fudan University. My advisor is Prof. Meng Chen.

My research interest lies in Biratioanl Algebraic Geometry, especially Higher Dimensional Boundedness Theory. Recently, I work on Boundedness of klt stable minimal models. I also work on explicit birational geometry, for example, calculating explicit effective birationality and lower bound of volumes of epsilon-lc polarized surfaces and threefolds. If you also have interests in these topics, please kindly contact me by e-mail.

selected publications

Preprint

Boundedness of polarized log Calabi-Yau fibrations with bounded bases

Xiaowei Jiang, Junpeng Jiao, and Minzhe Zhu

Apr 2025

arXiv:2504.05243

Abs arXiv

We investigate the boundedness problem for log Calabi-Yau fibrations whose bases and general fibers are bounded. We prove that the total spaces of log Calabi-Yau fibrations are bounded in codimension one after fixing some natural invariants. We also prove that the total spaces are bounded if, in addition, the irregularity of the general fibers vanishes. Then we apply our results to the boundedness problem for stable minimal models and fibered Calabi-Yau varieties.
IMRN

Boundedness of stable minimal models with klt singularities

Minzhe Zhu

International Mathematics Research Notices, Jan 2025

Abs DOI PDF

We investigate the singularities and boundedness of a special kind of algebraic varieties so-called stable minimal models, which are constructed and studied by Birkar. Given a klt stable minimal model with bounded relative volume, if we fix the dimension, Iitaka volume, and a DCC set controlling coefficients, then we show that the singularities of the klt stable minimal model can be controlled uniformly. Furthermore, we prove that with certain bounded data, stable minimal models with klt singularities form a bounded family.