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Jet schemes and minimal embedded desingularization of plane branches

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Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas Aims and scope Submit manuscript

Abstract

For a plane branch C with g Puiseux pairs, we determine the irreducible components of its jet schemes which correspond to the star (or rupture) and end divisors that appear on the dual graph of the minimal embedded desingularization of C. We exploit these informations to construct a Teissier type resolution of C embedded in \({\mathbb{C}^{g+1}}\), which is special in the sense that its restriction to the strict transform of the plane induces the minimal embedded desingularization of C.

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Authors and Affiliations

  1. CNRS, Laboratoire de Mathématiques de Versailles, 45 Avenue des Etas Unies, 78035, Versailles, France

    Monique Lejeune-Jalabert

  2. Institut de Mathématiques de Jussieu, Université Paris 7, 175 rue Chevaleret, 75013, Paris, France

    Hussein Mourtada

  3. Dpto. De lgebra y Geometra, Univ. Valladolid, 47005, Valladolid, Spain

    Ana Reguera

Authors
  1. Monique Lejeune-Jalabert
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  2. Hussein Mourtada
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  3. Ana Reguera
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Correspondence to Hussein Mourtada.

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To Professor Heisuke Hironaka on the occasion of his 80th birthday

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Lejeune-Jalabert, M., Mourtada, H. & Reguera, A. Jet schemes and minimal embedded desingularization of plane branches. RACSAM 107, 145–157 (2013). https://doi.org/10.1007/s13398-012-0091-5

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  • DOI: https://doi.org/10.1007/s13398-012-0091-5

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