会议议题(Agenda)
(1)阿贝尔簇概述以及Hodge猜想结论综述;
(2)阿贝尔曲面上层的模空间理论;
(3)带有复乘的阿贝尔簇的刻画;
(4)4维阿贝尔簇上的Hodge猜想;
(5)从杨-米尔斯方程的形变看Hodge猜想。
举办意义(Significance)
Hodge 猜想属于代数几何的领域,在数学中的著名猜想,很多数学家比如Hodge、Grothendieck、Deligne、Bloch、Voisin等围绕这个猜想发展了系统的理论并且引申了新的问题。Hodge猜想预测一个有理系数的上同调类如果其Hodge型达到代数链的预期那么它对应代数链的上同调类。
阿贝尔簇是非常特殊的代数簇,具有复乘结构的代数簇预期带有更多的代数链,所以人们首先探讨这类代数簇是否满足Hodge猜想。近年来,通过考察阿贝尔簇上特定对象的模空间,Markman等数学家用Fourier-Mukai变换的技术构造了自然代数闭链,这为探索Hodge猜想提供了新的思路。
这次研讨会将总结阿贝尔簇上Hodge猜想的进展,然后研讨目前的研究方法,探索能够突破的方向。
这次研讨会的参与者都有自己的研究领域,包括双有理几何、Higgs丛、代数簇的拓扑等等,还有很多学生参与,这次研讨会将会地促进领域间的交流并且培养一批学生未来持续研究这个方向的学生。
Maosheng,Tsinghua University
Lei Zhang, University of Science and Technology of China
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