# The intersection form on moduli spaces of twisted \$\$PGL_n\$\$PGLn-Higgs bundles vanishes

```@article{Heinloth2016TheIF,
title={The intersection form on moduli spaces of twisted \\$\\$PGL_n\\$\\$PGLn-Higgs bundles vanishes},
author={Jochen Heinloth},
journal={Mathematische Annalen},
year={2016},
volume={365},
pages={1499-1526}
}```
• Jochen Heinloth
• Published 2016
• Mathematics
• Mathematische Annalen
• Hausel and Rodriguez-Villegas conjectured that the intersection form on the moduli space of stable \$\$\textsf {PGL}_n\$\$PGLn-Higgs bundles on a curve vanishes if the degree is coprime to n. In this note we prove this conjecture. Along the way we show that moduli spaces of stable chains are irreducible for stability parameters larger than the stability condition induced form stability of Higgs bundles.

#### References

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