The maximal-minor F-threshold formula for large determinantal rings

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Let R=S/It(X)R=S/I_t(X), where XX is an n×mn\times m matrix of indeterminates, t=m≤nt=m\leq n, and cm(m)c^{\mathfrak{m}}(\mathfrak{m}) denotes the F-threshold of the homogeneous maximal ideal. The preceding results give the upper bound cm(m)≤n(t−12)c^{\mathfrak{m}}(\mathfrak{m})\leq n(t-\frac{1}{2}). Maximal-minor F-threshold conjecture. In the context of this upper bound, cm(m)=n(t−1)c^{\mathfrak{m}}(\mathfrak{m})=n(t-1) for all t,n≥5t,n\geq 5. This extends the formula proved in the paper for t=m∈{3,4}t=m\in\{3,4\}; the cases with both parameters at least 55 remain conjectural.

References

Primary source

Barbara Betti, Alessio Moscariello, Francesco Romeo and Jyoti Singh, “F-threshold of determinantal rings”, arXiv:2309.17376 (2023).

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