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Fourier-Mukai partners and autoequivalences of moduli spaces of vector bundles

  • Haotian Zuo
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Abstract

We classify the smooth projective Fourier--Mukai partners and determine the derived autoequivalence group of the moduli space UC(r,d) of stable bundles of coprime rank r≥2 and degree d on a smooth complex projective curve, assuming g(C)≥3 and Aut(C)=1. When the Jacobian J(C) has endomorphism ring Z, the partners are indexed by (Z/rZ)×/{±1}. We also prove that two coprime moduli spaces of vector bundles over complex curves of genus at least four are derived equivalent if and only if they are isomorphic.

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Cite

BibTeXRIS
BibTeX
@misc{zuo2026fouriermukai,
  title = {{Fourier-Mukai partners and autoequivalences of moduli spaces of vector bundles}},
  author = {Haotian Zuo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.30435},
  eprint = {2609.30435},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.30435},
}
RIS
TY  - UNPB
TI  - Fourier-Mukai partners and autoequivalences of moduli spaces of vector bundles
AU  - Haotian Zuo
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.30435
UR  - https://arxiv.org/abs/2609.30435
AB  - We classify the smooth projective Fourier--Mukai partners and determine the derived autoequivalence group of the moduli space U_C(r,d) of stable bundles of coprime rank r≥2 and degree d on a smooth complex projective curve, assuming g(C)≥3 and Aut(C)=1. When the Jacobian J(C) has endomorphism ring Z, the partners are indexed by (Z/rZ)^×/{±1}. We also prove that two coprime moduli spaces of vector bundles over complex curves of genus at least four are derived equivalent if and only if they are isomorphic.
ER  -