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math.AC2023
Deformations of local Artin rings via Hilbert-Burch matrices
Roser Homs, Anna-Lena Winz
In the local setting, Gröbner cells are affine spaces that parametrize ideals in that share the same leading term ideal with respect to a local term orderin…
math.AC2020
Canonical Hilbert-Burch matrices for power series
Roser Homs, Anna-Lena Winz
Sets of zero-dimensional ideals in the polynomial ring that share the same leading term ideal with respect to a given term ordering are known to be affine spaces called Gr…
math.AC2020
Primary ideals and their differential equations
Yairon Cid-Ruiz, Roser Homs, Bernd Sturmfels
An ideal in a polynomial ring encodes a system of linear partial differential equations with constant coefficients. Primary decomposition organizes the solutions to the PDE. This p…