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Representation Type of Rational ACM Surfaces \(\boldsymbol{X\subseteq\mathbb{P}^4}\)

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Abstract

The goal of this work is to determine the representation type of any smooth rational ACM surface in ℙ4 by constructing large families of simple Ulrich bundles of arbitrary rank. It turns out that, excluding the cubic scroll, all of them are of wild representation type. In addition, we show that a general linear standard determinantal variety of codimension one or two supports indecomposable Ulrich sheaves of rank 1 and 2.

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Authors and Affiliations

  1. Department d’Algebra i Geometria, Facultat de Matemàtiques, Gran Via des les Corts Catalanes 585, 08007, Barcelona, Spain

    Rosa M. Miró-Roig & Joan Pons-Llopis

  2. Departamento de Álgebra, Facultad de Matemáticas, Plaza de las Ciencias 3, 28040, Madrid, Spain

    Joan Pons-Llopis

Authors
  1. Rosa M. Miró-Roig
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  2. Joan Pons-Llopis
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Corresponding author

Correspondence to Joan Pons-Llopis.

Additional information

R. M. Miró-Roig was partially supported by MTM2010-15256.

J. Pons-Llopis was supported by the research project MTM2009-06964.

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Miró-Roig, R.M., Pons-Llopis, J. Representation Type of Rational ACM Surfaces \(\boldsymbol{X\subseteq\mathbb{P}^4}\) . Algebr Represent Theor 16, 1135–1157 (2013). https://doi.org/10.1007/s10468-012-9349-z

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  • DOI: https://doi.org/10.1007/s10468-012-9349-z

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