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Simpson filtration and oper stratum conjecture

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Abstract

In this paper, we prove that for the oper stratification of the de Rham moduli space \(M_{\mathrm {dR}}(X,r)\), the closed oper stratum is the unique minimal stratum with minimal dimension \(r^2(g-1)+g+1\), and the open dense stratum consisting of irreducible flat bundles with stable underlying vector bundles is the unique maximal stratum.

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Notes

  1. We say two semistable Higgs bundles are S-equivalent if their associated graded Higgs bundles defined by the Jordan-Hölder filtrations are isomorphic.

  2. Details on these invariants can be found in Simpson’s paper [30] (see also the second named author’s thesis [20]).

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Acknowledgements

The authors would like to express their deep gratitude to Prof. Brian Collier, Prof. Peter Gothen, Prof. Jochen Heinloth and Prof. Richard Wentworth for communications on various occasions, and to the anonymous referee for many valuable suggestions. The author P. Huang would like to thank Prof. Carlos Simpson for kind help and useful discussions, and thank Prof. Jiayu Li for his continuous encouragement.

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Authors and Affiliations

  1. School of Science, Nanjing University of Science and Technology, Nanjing, 210094, China

    Zhi Hu

  2. Department of Mathematics, Mainz University, 55128, Mainz, Germany

    Zhi Hu

  3. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, China

    Pengfei Huang

  4. Laboratoire J.A. Dieudonné, Université Côte d’Azur, CNRS, 06108, Nice, France

    Pengfei Huang

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  1. Zhi Hu
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  2. Pengfei Huang
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Hu, Z., Huang, P. Simpson filtration and oper stratum conjecture. manuscripta math. 167, 653–673 (2022). https://doi.org/10.1007/s00229-021-01286-7

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