A Fröberg type theorem for higher secant complexes

Abstract

We generalize the celebrated Fröberg's theorem to embedded joins of copies of a simplicial complex, namely higher secant complexes to the simplicial complex, in terms of property $N_{q+1,p}$ due to Green and Lazarsfeld. Furthermore, we investigate combinatorial phenomena parallel to geometric ones observed for higher secant varieties of minimal degree.

29 pages, Theorem 1.9 has been revised