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Ulrich Bundles on Veronese Surfaces

In: Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics

Author

Listed:
  • Laura Costa

    (Facultat de Matemàtiques i Informàtica, Departament de Matemàtiques i Informàtica)

  • Rosa Maria Miró-Roig

    (Facultat de Matemàtiques i Informàtica, Departament de Matemàtiques i Informàtica)

Abstract

It is a longstanding problem to determine whether the d-uple Veronese embedding of ℙ k $${\mathbb {P}}^k$$ supports a rank r Ulrich bundle. In this short note, we explicitly determine the integers d and r such that rank r Ulrich bundles on ℙ 2 $${\mathbb {P}}^2$$ for the Veronese embedding O ( d ) $${\mathcal {O}}(d)$$ exist and, in particular, we solve Conjecture A.1 in Coskun and Genc (Proc Am Math Soc 145:4687–4701, 2017).

Suggested Citation

  • Laura Costa & Rosa Maria Miró-Roig, 2018. "Ulrich Bundles on Veronese Surfaces," Springer Books, in: Gert-Martin Greuel & Luis Narváez Macarro & Sebastià Xambó-Descamps (ed.), Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics, pages 375-381, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-96827-8_14
    DOI: 10.1007/978-3-319-96827-8_14
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