Yonghwa Cho, Nodal Sextics and Even Sets of Nodes

It is a classical question to ask how many nodes may a surface contain. For sextics, the maximum number of nodes is 65, and is attained by Barth’s example. We ask further: are all sextics with 65 nodes like Barth’s example? To find an answer, we study even sets of nodes on sextic surfaces, and prove that all sextics with 65 nodes share the same structure of even sets. This establishes a resemblance between Barth’s sextic and other sextics with 65 nodes. This talk is based on a joint work with Fabrizio Catanese, Michael Kiermaier, and Sascha Kurz.