In this short note we show that for any pair of positive integers (d, n) with n > 2 and d > 1 or n = 2 and d > 4, there always exist projective varieties X ⊆ ℙN of dimension n and degree d and an integer s0 such that Hilbs(X) is reducible for all s ≥ s0. X will be a projective cone in ℙN over an arbitrary projective variety Y ⊆ ℙN-1. In particular, we show that, opposite to the case of smooth surfaces, there exist projective surfaces with a single isolated singularity which have reducible Hilbert scheme of points. © 2013 Copyright Taylor and Francis Group, LLC.

Reducibility of Punctual Hilbert Schemes of Cone Varieties / Miro-Roig, R. M.; PONS LLOPIS, JUAN FRANCISCO. - In: COMMUNICATIONS IN ALGEBRA. - ISSN 0092-7872. - 41:5(2013), pp. 1776-1780. [10.1080/00927872.2011.651756]

Reducibility of Punctual Hilbert Schemes of Cone Varieties

Pons-Llopis Juan Francisco
2013

Abstract

In this short note we show that for any pair of positive integers (d, n) with n > 2 and d > 1 or n = 2 and d > 4, there always exist projective varieties X ⊆ ℙN of dimension n and degree d and an integer s0 such that Hilbs(X) is reducible for all s ≥ s0. X will be a projective cone in ℙN over an arbitrary projective variety Y ⊆ ℙN-1. In particular, we show that, opposite to the case of smooth surfaces, there exist projective surfaces with a single isolated singularity which have reducible Hilbert scheme of points. © 2013 Copyright Taylor and Francis Group, LLC.
File in questo prodotto:
File Dimensione Formato  
Reducibility of Punctual Hilbert Schemes of Cone Varieties.pdf

non disponibili

Descrizione: articolo principale
Tipologia: 2a Post-print versione editoriale / Version of Record
Licenza: Non Pubblico - Accesso privato/ristretto
Dimensione 277.71 kB
Formato Adobe PDF
277.71 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11583/2859420