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PreprintCC0arXiv

Butler's conjecture for K3 curves

  • Soheyla Feyzbakhsh
  • Aliaksandra Novik
  • Angela Ortega
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Abstract

Butler's conjectures predict that, on a general smooth curve C of genus g≥3, a general coherent system [𝒪C⊗ VxrightarrowφE] with semistable underlying bundle E and dim V>rk(E) has surjective evaluation map φ and stable kernel. In this paper, we prove Butler's conjectures for g≥8 in the two cases in which the Brill-Noether geometry of a general curve is known, namely rank one and the range μ(E)>2g−2. By deformation and openness, it suffices to establish the result on a single Brill-Noether-Petri general curve. We do so for curves on K3 surfaces of Picard rank one, using the wall-crossing theory of coherent systems developed by the first two authors.

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Cite

BibTeXRIS
BibTeX
@misc{feyzbakhsh2026butlers,
  title = {{Butler's conjecture for K3 curves}},
  author = {Soheyla Feyzbakhsh and Aliaksandra Novik and Angela Ortega},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.08333},
  eprint = {2611.08333},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.08333},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Butler's conjecture for K3 curves
AU  - Soheyla Feyzbakhsh
AU  - Aliaksandra Novik
AU  - Angela Ortega
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.08333
UR  - https://arxiv.org/abs/2611.08333
AB  - Butler's conjectures predict that, on a general smooth curve C of genus g≥3, a general coherent system [𝒪_C⊗ VxrightarrowφE] with semistable underlying bundle E and dim V>rk(E) has surjective evaluation map φ and stable kernel. In this paper, we prove Butler's conjectures for g≥8 in the two cases in which the Brill-Noether geometry of a general curve is known, namely rank one and the range μ(E)>2g−2. By deformation and openness, it suffices to establish the result on a single Brill-Noether-Petri general curve. We do so for curves on K3 surfaces of Picard rank one, using the wall-crossing theory of coherent systems developed by the first two authors.
ER  -