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Exceptional hereditary curves and real curve orbifolds

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arxiv 2411.06222 v2 pith:FA7O5EZ7 submitted 2024-11-09 math.AG math.RT

Igor Burban This is my paper · ORCID
classification math.AGmath.RT
keywords curvecurveshereditaryexceptionalrealarbitrarycasecategory
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In this paper, we elaborate the theory of exceptional hereditary curves over arbitrary fields. In particular, we study the category of equivariant coherent sheaves on a regular projective curve whose quotient curve has genus zero and prove existence of a tilting object in this case. We also give a link between wallpaper groups and real hereditary curves, providing details to an old observation made by Helmut Lenzing.

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  1. Categorical absorption for hereditary orders

    math.AG 2025-05 conditional novelty 6.0 of 10

    A hereditary order on a curve is shown to admit a strong C-linear semiorthogonal decomposition obtained from the deformation absorption of singularities in its fiber over a ramified point.

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