Analogy with the moduli space of Higgs bundles

Analogy with the moduli space of Higgs bundles 

The Hilbert scheme is analogous in many ways with the moduli space of Higgs 

Let E be a compact Riemann surface. The moduli space As of Higgs bundle over E is dehned by 

We shall not explain what the stability condition means. The interested reader may consult the original papers [36, 37] for the precise definition and the properties of A/s mentioned in the following. 

Now we shall explain how much T E[ 1 looks like A/s- In both cases, there exists a holomorphic symplectic form ujc and a C -action which satisfies 4 luJc = for t E C. The holomorphic symplectic form on As is given as follows. For (, ) G A/s, the tangent space of As at E, ) is given by 

The Hilbert scheme T is analogous in many ways with the moduli space of Higgs bundle over a Riemann surface introduced by Hitchin [36]. 

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ANALOGY WITH THE MODULI SPACE OF HIGGS BUNDLES... 

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