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October 20, 2025Open Access

A note on the Brill-Noether loci of small codimension in moduli space of stable bundles

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Authors

PBPritthijit BiswasJIJaya NN Iyer

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Overview

Analysis shows Brill-Noether loci are stably-rational for g=3 and unirational for g=4, indicating interesting properties in moduli space.

Key Points

  • The Brill-Noether locus W^{1}_{X}(2,L) is stably-rational for curves of genus 3, which suggests a deeper geometric structure.
  • For genus 4, it is unirational, showing that these spaces enlarge the understanding of stable bundles.
  • For genus 5 and higher, W^{1}_{X}(2,L) is rationally chain connected by Hecke curves, linking these algebraic structures via geometric objects.
  • Triviality of low dimensional rational Chow groups indicates potential simplifications in computing intersection theory in these moduli spaces.

Cite This Study

Biswas et al. (2025) studied this question.

synapsesocial.com/papers/68f5c338e2d8b12842645bfchttps://doi.org/10.48550/arxiv.2505.15749
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