【学术报告】Singular irreducible symplectic surfaces

报告人：Matteo Penegini（意大利帕维亚大学）

时 间：2025年12月10日9:30

地 点：海韵园实验楼S204

内容摘要:

To extend the Beauville-Bogomolov decomposition theorem, we need to define the singular versions of irreducible holomorphic symplectic manifolds, known as "singular irreducible symplectic varieties." These are compact, connected complex varieties with canonical singularities that possess a holomorphic symplectic form σ on the smooth locus, and for which every finite quasi-étale covering has its algebra of reflexive forms spanned by the reflexive pull-back of σ. We classify all singular irreducible symplectic surfaces, which are essentially contractions of ADE configurations of curves on K3 surfaces. We describe the families of these surfaces, categorizing them into two classes: those that do not admit any quasi-étale coverings, and those that do, necessarily with a K3 surface. Finally, we briefly discuss the Hilbert scheme of two points on these surfaces.

个人简介：

Matteo Penegini，意大利帕维亚大学副教授。2010年博士毕业于德国拜罗伊特大学，研究方向是代数几何，研究兴趣包括复曲面（特别是一般型曲面与K3曲面），一般型三维簇的地理问题等，论文发表在Trans AMS, IMRN, Rev. Mat. Iberoam., J. Lond. Math. Soc., Nagoya Math. J. 等期刊上。

联系人：刘文飞