A Fr\"{o}berg type theorem for higher secant complexes
Commutative Algebra
2025-05-19 v2 Algebraic Geometry
Combinatorics
Abstract
We generalize the celebrated Fr\"{o}berg's theorem to embedded joins of copies of a simplicial complex, namely higher secant complexes to the simplicial complex, in terms of property due to Green and Lazarsfeld. Furthermore, we investigate combinatorial phenomena parallel to geometric ones observed for higher secant varieties of minimal degree.
Cite
@article{arxiv.2502.20987,
title = {A Fr\"{o}berg type theorem for higher secant complexes},
author = {Junho Choe and Jaewoo Jung},
journal= {arXiv preprint arXiv:2502.20987},
year = {2025}
}
Comments
29 pages, Theorem 1.9 has been revised