工作营介绍：

形变理论研究几何空间在全纯变化中的结构演化，Hodge理论为其提供了核心工具。在双有理几何中，形变理论发挥着关键作用，反过来，双有理几何的发展也为形变问题提供了有力的方法。例如，abundance猜想与极小模型纲领的实现可推导出多亏格的形变不变性。本次工作营将围绕多亏格形变不变性、高维Shafarevich纲领、极小有理切线簇以及双有理几何中的有界性等前沿课题展开深入探讨。

时间：2025年7月6日—18日

地点：国家天元数学中部中心恩施基地 湖北民族大学

日程安排：

报告信息：

VMRT theory and beyond

丁聪

深圳大学

The theory of variety of minimal rational tangents, introduced by Hwang and Mok, has been used to solve lots of problems in algebraic geometry, e.g., the Kähler deformation rigidity of irreducible Hermitian symmetric spaces and the Lazarsfeld problem. In this short course, I will review some basic notions, examples and techniques in VMRT theory. Also, I will talk about a recent development of the so-called sub-VMRT theory, which was introduced by Mok and Zhang, and its applications in the rigidity problems of Schubert cycles. Moreover, I will discuss its interesting relations with some other areas, especially in several complex variables (e.g. rigidity of holomorphic isometric embeddings) and Hodge theory (e.g. Griffiths–Yukawa couplings). In the meantime, some open problems will be discussed.

Boundedness in birational geometry

焦骏鹏

清华大学

In this series, we explore boundedness results for fundamental classes of higher-dimensional algebraic varieties, focusing on canonically polarized varieties and Fano varieties.

Moishezon spaces and Moishezon morphisms

李义

武汉大学

This course is an introduction to Moishezon spaces and Moishezon morphisms. We first introduce some basic notions related to Moishezon varieties and Moishezon morphisms. We then go into various research topics related to them, including the invariance of plurigenera in the Moishezon setting, the general type locus and the Moishezon locus, fiberwise bimeromorphic morphisms, the deformation openness of the projectivity condition, and rational curves on Moishezon varieties.

Higher Dimensional Shafarevich Program

孙锐然

厦门大学

Moduli theory is a central branch of algebraic geometry dedicated to understanding how algebraic varieties deform and degenerate. Studying the geometry of a moduli stack tells a lot about these properties. In 1962, I. R. Shafarevich formulated influential conjectures concerning the moduli spaces of genus g curves, which have since had a significant impact on the development of both algebraic and arithmetic geometry. This short course will review the geometric aspects of Shafarevich's original conjecture and explore the subsequent study of algebraic fiber spaces and the geometry of higher-dimensional moduli spaces, guided by generalizations of Shafarevich's vision. Key topics include: construction of moduli space, Viehweg-Zuo big subsheaf and its application to hyperbolicity problems, Arakelov type inequality, characteristic bundles/varieties, and rigidity problems on moduli spaces.

组织者：

李木林（湖南大学）

饶  胜（武汉大学）

主办单位：

国家天元数学中部中心、武汉大学数学与统计学院