Abstract
Let $X$ be a compact Riemann surface of genus $g\geq 2$. In this paper we study how two memorable stratifications of the moduli space of Higgs bundles of rank $4$ over $X$, Shatz stratification and Bialynicki-Birula stratification, relate to each other and provide dimensions for the Harder-Narasimhan type of a semistable rank 4 Higgs bundle over $X$. In particular, we prove that the two stratifications do not coincide. Thus, we extend to rank 4 the work of Hausel [7], who proved that both stratifications coincide in rank 2, and of Gothen and Zúñiga-Rojas [6], who proved that such a thing no longer occurred in rank 3.
Citation
Álvaro ANTÓN SANCHO. "Shatz and Bialynicki-Birula stratifications of the moduli space of Higgs bundles." Hokkaido Math. J. 51 (1) 25 - 56, February 2022. https://doi.org/10.14492/hokmj/2019-202
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