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<p>We functorially identify similarity classes of line-bundle-valued quadratic forms on rank two vector bundles with isomorphism classes of pairs consisting of the degree zero and the degree one parts of the associated generalized Clifford algebras. As applications, we generalize the Gauss Composition and explore connections with Picard groups of quadratic algebras.</p>

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Classifying binary quadratic forms using clifford invariants

  • 期刊论文

  • 发表日期：

    2026年7月17日

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  • Soham Mondal,
  • Venkata Balaji Thiruvalloor Eesanaipaadi

摘要

We functorially identify similarity classes of line-bundle-valued quadratic forms on rank two vector bundles with isomorphism classes of pairs consisting of the degree zero and the degree one parts of the associated generalized Clifford algebras. As applications, we generalize the Gauss Composition and explore connections with Picard groups of quadratic algebras.