Reduction numbers of links of irreducible varieties
Alberto Corso, Claudia polini
Abstract
The reductions of an ideal I give a natural pathway to the properties of I, with the advantage of having fewer generators. In this paper we primarily focus on a conjecture about the reduction exponent of links of a broad class of primary ideals. The existence of an algebra structure on the Koszul and Eagon-Northcott resolutions is the main tool for detailing the known cases of the conjecture. In the last section we relate the conjecture to a formula involving the length of the first Koszul homology modules of these ideals.
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