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On the Briançon-Skoda theorem on a singular variety

Mats Andersson, Håkan Samuelsson, Jacob Sznajdman (2010)

Annales de l’institut Fourier

Let Z be a germ of a reduced analytic space of pure dimension. We provide an analytic proof of the uniform Briançon-Skoda theorem for the local ring 𝒪 Z ; a result which was previously proved by Huneke by algebraic methods. For ideals with few generators we also get much sharper results.

On the canonical ideal of a set of points

Martin Kreuzer (2000)

Bollettino dell'Unione Matematica Italiana

Dato un insieme X di s punti nello spazio proiettivo, si costruisce un esplicito ideale canonico I nel suo anello di coordinate R . Si descrivono le componenti omogenee di I e la struttura della mappa di moltiplicazione R σ I σ + 1 I 2 σ + 1 , dove σ = max i H X i < s . Tra le applicazioni ci sono varie caratterizzazioni di insiemi di punti coomologicamente uniformi, disuguaglianze nelle loro funzioni di Hilbert, il calcolo del primo modulo delle sizigie di I in casi particolari, una generalizzazione della «trasformata di Gale» a trasformate...

On the closed subfields of [...] Q ¯   p Q ¯ ˜ p

Sever Achimescu, Victor Alexandru, Corneliu Stelian Andronescu (2016)

Open Mathematics

Let p be a prime number, and let [...] Q¯ p Q ¯ ˜ 𝐩 be the completion of Q with respect to the pseudovaluation w which extends the p-adic valuation vp. In this paper our goal is to give a characterization of closed subfields of [...] Q¯ p Q ¯ ˜ 𝐩 , the completion of Q with respect w, i.e. the spectral extension of the p-adic valuation vp on Q.

On the generalized Davenport constant and the Noether number

Kálmán Cziszter, Mátyás Domokos (2013)

Open Mathematics

Known results on the generalized Davenport constant relating zero-sum sequences over a finite abelian group are extended for the generalized Noether number relating rings of polynomial invariants of an arbitrary finite group. An improved general upper degree bound for polynomial invariants of a non-cyclic finite group that cut out the zero vector is given.

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