Special lines on cubic fourfolds

Location: 11th Floor Lecture Hall Speaker Yilong Zhang, University of Georgia Session Chair Asher Auel, Dartmouth College Abstract Lines on cubic hypersurfaces were studied by Clemens and Griffiths in the 1970s. There are two types of lines, depending on their normal bundles. In this talk, I’ll introduce a new type of special line on cubic fourfolds, called a “higher triple line.” Cubic fourfolds containing such lines form a codimension-one subfamily of smooth cubic fourfolds. I’ll discuss how this relates to a problem concerning Hilbert schemes on cubic fourfolds.