Properties of analogues of Frobenius powers of ideals

Subhajit Chanda () and Arvind Kumar ()
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Subhajit Chanda: New Academic Complex, IIT Madras
Arvind Kumar: Chennai Mathematical Institute

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 2, 524-531

Abstract: Abstract Let $$R=\mathbb {K}[X_1, \ldots , X_n ]$$ R = K [ X 1 , … , X n ] be a polynomial ring over a field $$\mathbb {K}$$ K . We introduce an endomorphism $$\mathcal {F}^{[m]}: R \rightarrow R $$ F [ m ] : R → R and denote the image of an ideal I of R via this endomorphism as $$I^{[m]}$$ I [ m ] and call it to be the m-th square power of I. In this article, we study some homological invariants of $$I^{[m]}$$ I [ m ] such as regularity, projective dimension, associated primes, and depth for some families of ideals, e.g., monomial ideals.

Keywords: Frobenius power; Square power; Regularity; Projective dimension; Betti numbers; Depth and symbolic power; 13A35; 13D02; 13F55 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00272-3

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