Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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HECKE CURVES IN FROBENIUS STRATA OF MODULI SPACE OF RANK 2 VECTOR BUNDLES

  • Lingguang Li (School of Mathematical Sciences Tongji University Key Laboratory of Intelligent Computing and Applications (Tongji University) Ministry of Education) ;
  • Hongyi Zhang (School of Mathematical Sciences Tongji University Key Laboratory of Intelligent Computing and Applications (Tongji University) Ministry of Education)
  • Received : 2025.07.12
  • Accepted : 2026.04.06
  • Published : 2026.07.31
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Abstract

Let k be an algebraically closed field with characteristic 2, and let X be a smooth projective algebraic curve of genus g ⩾ 2 over k. Let 𝓜sX (2, 𝓛) be the moduli space of rank 2 stable vector bundles with determinant 𝓛 on X. The Frobenius stratification measures the instability of bundles in 𝓜sX(r, 𝓛) under pullback by the Frobenius map. We show that there exists a Frobenius stratum in 𝓜sX(2, 𝓛) which is covered by Hecke curves.

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Acknowledgement

This work was supported by National Natural Science Foundation of China (Grant No. 12171352), Applied Basic Research Programs of Science and Technology Commission Foundation of Shanghai Municipality (22JC1402700).