A Saito criterion for holonomic divisors
Raul Epure, Mathias Schulze
TL;DR
This paper establishes a new criterion linking the freeness of holonomic divisors to the algebraic structure obtained from logarithmic derivations acting on generic functions with isolated critical points.
Contribution
It introduces a Saito criterion for holonomic divisors, connecting their freeness to complete intersection Artin algebras generated by logarithmic derivations.
Findings
Holonomic divisors are free iff a certain algebra is a complete intersection.
The criterion provides a new algebraic test for divisor freeness.
The result bridges differential and algebraic properties of divisors.
Abstract
We show that a holonomic divisor is free if and only if applying all logarithmic derivations to a generic function with isolated critical point yields a complete intersection Artin algebra.
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