Computing S(X) for Ruled Surfaces Defined by Stable Bundles on Curves of Genus 2

@misc{mcpherson2026computing,
  title = {{Computing S(X) for Ruled Surfaces Defined by Stable Bundles on Curves of Genus 2}},
  author = {Lillian McPherson},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.22573},
  eprint = {2610.22573},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.22573},
}

TY  - UNPB
TI  - Computing S(X) for Ruled Surfaces Defined by Stable Bundles on Curves of Genus 2
AU  - Lillian McPherson
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.22573
UR  - https://arxiv.org/abs/2610.22573
AB  - This paper discusses the algebra of symmetric tensors for ruled surfaces defined by rank 2 stable vector bundles on curves of genus 2. The algebra is computed for special bundles E when S^2 E is destabilized by a line bundle and when S^3 E is destabilized by a bundle of rank 2. A strategy for computation is discussed in regards to the other special bundles E. This paper also discusses the generalization of these strategies to higher genus and gives a computation when E is not stable and may be written as a direct sum of line bundles.
ER  -