Pathologies on the Hilbert scheme of points

• 成果类型: Article
• 署名作者: Jelisiejew, Joachim
• 署名单位: Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; University of Warsaw
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-019-00939-5
• 发表日期: 2020
• 页码: 581-610
• 关键词: murphys-law; SPACE

摘要

We prove that the Hilbert scheme of points on a higher dimensional affine space is non-reduced and has components lying entirely in characteristic p for all primes p. In fact, we show that Vakil's Murphy's Law holds up to retraction for this scheme. Our main tool is a generalized version of the Bialynicki-Birula decomposition.