Minzhe Zhu

Office 1539, Korea Institute for Advanced Study

85 Hoegiro, Dongdaemun-gu

Seoul, Korea

Hi! I am a research fellow at the Korea Institute for Advanced Study(KIAS). I obtained my Ph.D. at Fudan University under the supervision of Prof. Meng Chen.

My research interests lie in birational algebraic geometry, with a particular focus on higher-dimensional boundedness theory. My recent work includes the boundedness of polarized log Calabi–Yau fibrations and klt stable minimal models. I am also interested in explicit birational geometry, such as effective birationality and explicit lower bounds for the volumes of $\epsilon$-lc polarized surfaces and threefolds. If you are interested in these topics, please feel free to contact me by e-mail.

selected publications

JEMS

Boundedness of polarized log Calabi-Yau fibrations with bounded bases

Xiaowei Jiang, Junpeng Jiao, and Minzhe Zhu

Journal of the European Mathematical Society, 2025

To appear

Abs arXiv PDF

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.