Mixing
Use of GIT for moduli problems
1
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Was there an actual use of GIT technics (moment map, Kempf-Ness theorem) in the different proofs of the Kobayashi-Hitchin correspondence (by Uhlenbeck-Yau and Donaldson)? Or this was rather a heuristic to a hardcore analytical proof.
complex-geometry gauge-theory geometric-invariant-theory
asked Jan 28 at 17:14
BinAckerBinAcker
315
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1
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Was there an actual use of GIT technics (moment map, Kempf-Ness theorem) in the different proofs of the Kobayashi-Hitchin correspondence (by Uhlenbeck-Yau and Donaldson)? Or this was rather a heuristic to a hardcore analytical proof.
complex-geometry gauge-theory geometric-invariant-theory
asked Jan 28 at 17:14
BinAckerBinAcker
315
$endgroup$
1
$begingroup$
I just looked at the Uhlenbeck-Yau paper and no GIT ever appears. They construct this metric as a limit, and in showing that this limit exists, they need a uniform bound on the size of something. In showing this bound, they use the stability condition: they show that a consequence of this size blowing up is that there is a subsheaf of $E$ violating the stability condition. This starts on page 17. It has been a while since I looked at the Donaldson paper but again I think it is completely independent of algebraic geometry.
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– user98602
Jan 28 at 22:28
add a comment |
1
1
1
1
$begingroup$
Was there an actual use of GIT technics (moment map, Kempf-Ness theorem) in the different proofs of the Kobayashi-Hitchin correspondence (by Uhlenbeck-Yau and Donaldson)? Or this was rather a heuristic to a hardcore analytical proof.
complex-geometry gauge-theory geometric-invariant-theory
asked Jan 28 at 17:14
BinAckerBinAcker
315
$endgroup$
Was there an actual use of GIT technics (moment map, Kempf-Ness theorem) in the different proofs of the Kobayashi-Hitchin correspondence (by Uhlenbeck-Yau and Donaldson)? Or this was rather a heuristic to a hardcore analytical proof.
complex-geometry gauge-theory geometric-invariant-theory
complex-geometry gauge-theory geometric-invariant-theory
asked Jan 28 at 17:14
BinAckerBinAcker
315
asked Jan 28 at 17:14
BinAckerBinAcker
315
asked Jan 28 at 17:14
BinAckerBinAcker
315
asked Jan 28 at 17:14
BinAckerBinAcker
315
asked Jan 28 at 17:14
BinAckerBinAcker
315
315
1
$begingroup$
I just looked at the Uhlenbeck-Yau paper and no GIT ever appears. They construct this metric as a limit, and in showing that this limit exists, they need a uniform bound on the size of something. In showing this bound, they use the stability condition: they show that a consequence of this size blowing up is that there is a subsheaf of $E$ violating the stability condition. This starts on page 17. It has been a while since I looked at the Donaldson paper but again I think it is completely independent of algebraic geometry.
$endgroup$
– user98602
Jan 28 at 22:28
add a comment |
1
$begingroup$
I just looked at the Uhlenbeck-Yau paper and no GIT ever appears. They construct this metric as a limit, and in showing that this limit exists, they need a uniform bound on the size of something. In showing this bound, they use the stability condition: they show that a consequence of this size blowing up is that there is a subsheaf of $E$ violating the stability condition. This starts on page 17. It has been a while since I looked at the Donaldson paper but again I think it is completely independent of algebraic geometry.
$endgroup$
– user98602
Jan 28 at 22:28
1
1
$begingroup$
I just looked at the Uhlenbeck-Yau paper and no GIT ever appears. They construct this metric as a limit, and in showing that this limit exists, they need a uniform bound on the size of something. In showing this bound, they use the stability condition: they show that a consequence of this size blowing up is that there is a subsheaf of $E$ violating the stability condition. This starts on page 17. It has been a while since I looked at the Donaldson paper but again I think it is completely independent of algebraic geometry.
$endgroup$
– user98602
Jan 28 at 22:28
$begingroup$
I just looked at the Uhlenbeck-Yau paper and no GIT ever appears. They construct this metric as a limit, and in showing that this limit exists, they need a uniform bound on the size of something. In showing this bound, they use the stability condition: they show that a consequence of this size blowing up is that there is a subsheaf of $E$ violating the stability condition. This starts on page 17. It has been a while since I looked at the Donaldson paper but again I think it is completely independent of algebraic geometry.
$endgroup$
– user98602
Jan 28 at 22:28
add a comment |
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1
$begingroup$
I just looked at the Uhlenbeck-Yau paper and no GIT ever appears. They construct this metric as a limit, and in showing that this limit exists, they need a uniform bound on the size of something. In showing this bound, they use the stability condition: they show that a consequence of this size blowing up is that there is a subsheaf of $E$ violating the stability condition. This starts on page 17. It has been a while since I looked at the Donaldson paper but again I think it is completely independent of algebraic geometry.
$endgroup$
– user98602
Jan 28 at 22:28