Comparison theorems for deformation functors via invariant theory

被引：1

作者：

Christophersen, Jan Arthur ^{[1
]}

Kleppe, Jan O. ^{[2
]}

机构：

[1] Univ Oslo, Matemat Inst, Postboks 1053 Blindern, N-0316 Oslo, Norway

[2] Oslo Metropolitan Univ, Fac Technol Art & Design, PB 4 St Olavs Pl, N-0130 Oslo, Norway

来源：

COLLECTANEA MATHEMATICA | 2019年 / 70卷 / 01期

关键词：

Cotangent complex; Deformation theory; Hilbert groups; Reductive groups; Toric varieties; LOCAL COHOMOLOGY; CURVES; SPACES;

D O I：

10.1007/s13348-018-0232-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We compare deformations of algebras to deformations of schemes in the setting of invariant theory. Our results generalize comparison theorems of Schlessinger and the second author for projective schemes. We consider deformations (abstract and embedded) of a scheme X which is a good quotient of a quasi-affine scheme X by a linearly reductive group G and compare them to invariant deformations of an affine G-scheme containing X as an open invariant subset. The main theorems give conditions for when the comparison morphisms are smooth or isomorphisms.

引用

页码：1 / 32

页数：32

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