Secants, Socles and Stability
Commutative Algebra
2025-05-21 v1 Algebraic Geometry
Abstract
The projective space of symmetric tensors of degree d can be reinterpreted as a projective space of finite, graded Gorenstein rings with socle in degree d. Via a pair of explicit stability conditions (one for even values of d and one for odd values), the space of symmetric tensors is partitioned by Harder-Narasimhan filtration type. This is worked out explicitly for low degree examples in dimension three (the projective plane) and compared with the betti tables of the Gorenstein rings.
Cite
@article{arxiv.2505.14445,
title = {Secants, Socles and Stability},
author = {Aaron Bertram and Brooke Ullery},
journal= {arXiv preprint arXiv:2505.14445},
year = {2025}
}