Invariant deformation theory of affine schemes with reductive group action

Christian Lehn ^[1] ; Ronan Terpereau ^[2]
1. [1] University of Hannover
  
  University of Hannover
  
  Region Hannover, Alemania
2. [2] Johannes Gutenberg University of Mainz
  
  Johannes Gutenberg University of Mainz
  
  Kreisfreie Stadt Mainz, Alemania
Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 9 (September 2015), 2015, págs. 4168-4202
Idioma: inglés
DOI: 10.1016/j.jpaa.2015.02.013
Enlaces
- Texto completo
Resumen
- We develop an invariant deformation theory, in a form accessible to practice, for affine schemes W equipped with an action of a reductive algebraic group G. Given the defining equations of a G -invariant subscheme X⊂W, we device an algorithm to compute the universal deformation of X in terms of generators and relations up to a given order. In many situations, our algorithm even computes an algebraization of the universal deformation. As an application, we determine new families of examples of the invariant Hilbert scheme of Alexeev and Brion, where G is a classical group acting on a classical representation, and we describe their singularities