We prove that the generalized Hilbert-Kunz function of a graded module over a two-dimensional standard graded normal -domain over an algebraically closed field of prime characteristic has the form , with rational generalized Hilbert-Kunz multiplicity and a bounded function. Moreover, we prove that if is a -algebra, the limit for of the...
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2018 (v1)PublicationUploaded on: April 14, 2023
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2017 (v1)Publication
We define two related invariants for a d-dimensional local ring (R,,k) called syzygy and differential symmetric signature by looking at the maximal free splitting of reflexive symmetric powers of two modules: the top-dimensional syzygy module SyzdR(k) of the residue field and the module of Kähler differentials ΩR/k of R over k. We compute these...
Uploaded on: April 14, 2023 -
2019 (v1)Publication
We study the differential symmetric signature, an invariant of rings of finite type over a field, introduced in a previous work by the authors in an attempt to find a characteristic-free analogue of the F-signature. We compute the differential symmetric signature for invariant rings k[x1, . . ., xn]G, where G is a finite small subgroup of GL(n,...
Uploaded on: April 14, 2023 -
2019 (v1)Publication
We study the differential symmetric signature, an invariant of rings of finite type over a field, introduced in a previous work by the authors in an attempt to find a characteristic-free analogue of the F-signature. We compute the differential symmetric signature for invariant rings k[x(1), ... , x(n)](G), where G is a finite small subgroup of...
Uploaded on: February 14, 2024