Comparison theorems for deformation functors via invariant theory

• Autores: Jan Arthur Christophersen, Jan O. Kleppe
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 70, Fasc. 1, 2019, págs. 1-32
• Idioma: inglés
• DOI: 10.1007/s13348-018-0232-z
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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^\prime by a linearly reductive group G and compare them to invariant deformations of an affine G-scheme containing X^\prime as an open invariant subset. The main theorems give conditions for when the comparison morphisms are smooth or isomorphisms.

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