We give a simple proof for the fact that the CastelnuovoâMumford regularity and related invariants of products of powers of ideals are asymptotically linear in the exponents, provided that each ideal is generated by elements of constant degree. We provide examples showing that the asymptotic linearity is false in general. On the other hand, the regularity is always given by the maximum of finitely many linear functions whose coefficients belong to the set of the degrees of generators of the ideals.
A remark on regularity of powers and products of ideals
Conca, Aldo
2017-01-01
Abstract
We give a simple proof for the fact that the CastelnuovoâMumford regularity and related invariants of products of powers of ideals are asymptotically linear in the exponents, provided that each ideal is generated by elements of constant degree. We provide examples showing that the asymptotic linearity is false in general. On the other hand, the regularity is always given by the maximum of finitely many linear functions whose coefficients belong to the set of the degrees of generators of the ideals.File in questo prodotto:
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