# COMPUTING QUOTIENTS BY CONNECTED SOLVABLE GROUPS

Abstract : This paper introduces the notion of an excellent quotient, which is stronger than a universal geometric quotient. The main result is that for an action of a connected solvable group $G$ on an affine scheme Spec$(R)$ there exists a semi-invariant $f$ such that Spec$(R_f) \to$ Spec$((R_f)^G)$ is an excellent quotient. The paper contains an algorithm for computing $f$ and $(R_f)^G$. If $R$ is a polynomial ring over a field, the algorithm requires no Gr\"obner basis computations, and it also computes a presentation of $(R_f)^G$. In this case, $(R_f)^G$ is a complete intersection. The existence of an excellent quotient extends to actions on quasi-affine schemes
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Cited literature [25 references]

https://hal.inria.fr/hal-02912346
Contributor : Alain Monteil <>
Submitted on : Wednesday, August 5, 2020 - 4:45:30 PM
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Long-term archiving on: : Monday, November 30, 2020 - 3:03:59 PM

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• HAL Id : hal-02912346, version 1

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Gregor Kemper. COMPUTING QUOTIENTS BY CONNECTED SOLVABLE GROUPS. MEGA 2019 - International Conference on Effective Methods in Algebraic Geometry, Jun 2019, Madrid, Spain. ⟨hal-02912346⟩

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