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Vector bundles on singular surfaces and threefolds

  • Jean Fasel
  • Maria Yakerson
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Abstract

We fully classify vector bundles of critical rank on normal affine surfaces and threefolds over algebraically closed fields via their Chern classes. We also prove existence of rank $2$ bundles on threefolds with prescribed first and second motivic Chern classes. The main input is the motivic filtration on algebraic K-theory: its third piece is generated by smooth closed points and is identified with motivic cohomology by the third Chern class.

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Cite

BibTeXRIS
BibTeX
@misc{fasel2026vector,
  title = {{Vector bundles on singular surfaces and threefolds}},
  author = {Jean Fasel and Maria Yakerson},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.22679},
  eprint = {2610.22679},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05820411v1},
}
RIS
TY  - UNPB
TI  - Vector bundles on singular surfaces and threefolds
AU  - Jean Fasel
AU  - Maria Yakerson
PY  - 2026
DA  - 2026/10/15
PB  - HAL
DO  - 10.48550/arxiv.2610.22679
UR  - https://hal.science/hal-05820411v1
AB  - We fully classify vector bundles of critical rank on normal affine surfaces and threefolds over algebraically closed fields via their Chern classes. We also prove existence of rank $2$ bundles on threefolds with prescribed first and second motivic Chern classes. The main input is the motivic filtration on algebraic K-theory: its third piece is generated by smooth closed points and is identified with motivic cohomology by the third Chern class.
ER  -