Abstract: Nodes, or ordinary double points, are the most elementary singularities on curves and represent a cornerstone of classical algebraic geometry. Their significance is underscored by the Deligne–Mumford compactification of the moduli space of smooth curves, where they appear naturally on the boundary. An analogous framework exists in the moduli theory of higher-dimensional varieties, where this concept is generalized as "nodes in codimension-one". In this talk, we will review nodes from several perspectives, examine explicit examples, and discuss how this notion extends to higher dimensions.

 

Organizers: Harry Richman (NCTS) & Wille Liu (Academia Sinica)