Reducibility of Punctual Hilbert Schemes of Cone Varieties

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.

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Titolo: Reducibility of Punctual Hilbert Schemes of Cone Varieties
Autori: 
PONS LLOPIS, JUAN FRANCISCO
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Data di pubblicazione: 2013
Rivista: 
COMMUNICATIONS IN ALGEBRA  
Digital Object Identifier (DOI): http://dx.doi.org/10.1080/00927872.2011.651756
Appare nelle tipologie:1.1 Articolo in rivista

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