Moduli of linear slices of high degree smooth hypersurfaces

This paper, joint with E. Riedl and D. Tseng, further explores the maximal variation theme in my work, which began with this paper. In this case, we investigate how the moduli of a general hyperplane slice of a hypersurface X varies with small perturbations of the hyperplane. We prove that, as long as the degree of X is large enough, this variation is maximal for any smooth hypersurface X! (It is an easy exercise to prove the analogous statement for a general hypersurface X.)