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An intrinsic construction of the principal component of the Hilbert scheme
Author(s) -
Rydh David,
Skjelnes Roy
Publication year - 2010
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdq042
Subject(s) - principal component analysis , hilbert scheme , scheme (mathematics) , construct (python library) , component (thermodynamics) , property (philosophy) , mathematics , closure (psychology) , principal (computer security) , pure mathematics , computer science , mathematical analysis , physics , statistics , law , computer security , quantum mechanics , political science , philosophy , epistemology , programming language
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 étale families, from which the appropriate universal property, needed to identify the principal component with the blow‐up, is derived.