An intrinsic construction of the principal component of the Hilbert scheme
- Autores: David Rydh, Roy Mikael Skjelnes
- Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 82, Nº 2, 2010, págs. 459-481
- Idioma: inglés
- DOI: 10.1112/jlms/jdq042
- Enlaces
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Resumen
The principal component of the Hilbert scheme of n points on a scheme X is the closure of the open subset parameterizing n distinct points. In this article we construct the principal component as a certain blow-up of the symmetric product of X. Our construction is based on a local explicit analysis of ´etale families, from which the appropriate universal property, needed to identify the principal component with the blow-up, is derived.
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