GIT quotient

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- Tags: - #todo/untagged - Refs: - Kirwan’s paper: https://www.jstor.org/stable/pdf/1971369.pdf?refreqid=excelsior%3A3ec9b95300955f55a49084b50d539d45&ab_segments=&origin=&acceptTC=1#page=1 - Links: - #todo/create-links

GIT quotient

Main tools:

the numerical criterion,
Luna's slice theorem, and
Kirwan's desingularization

Motivation

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Summary

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Construction

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Constructing the ring of invariants

Uses a Reynolds operator attachments/Pasted%20image%2020220407201836.png

Geometric quotients

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Examples

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Misc

Sometimes dual to a VHS description: attachments/Pasted%20image%2020220523011857.png

Links to this page

unresolved links output

Reynolds operator in Unsorted/GIT quotient
moment map

GIT quotient
character variety

Comparing the character stack to the GIT (categorical) quotient:
Luna's slice theorem

GIT quotient
900_Changelog

2022-09-14 at 19h54 · GIT quotient
2021-11-03-quick_note

Define GIT quotient as \(X{ \mathbin{/\mkern-6mu/}}G\coloneqq\mathop{\mathrm{Proj}}\bigoplus _{i\geq 0} H^*(X; {\mathcal{L}}{ {}^{ \scriptscriptstyle\otimes_{k}^{i} } } )^G\), where by Hilbert if \(G\) is reductive then the invariants are finitely generated.

#todo/untagged #todo/create-links