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<p>Logarithmic vector fields along a singular curve and the Camacho-Sad-Suwa indices, generalizations of the Camacho-Sad index introduced by T. Suwa, are considered in the context of computational complex analysis. An effective algorithm is introduced for computing a basis of the module of germs of logarithmic vector fields along a given singular curve. A new method is described for computing the Camacho-Sad-Suwa indices. The keys of our approach are the use of local cohomology and Grothendieck local duality. Several examples are given for illustration.</p>

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Computing Camacho-Sad-Suwa indices of logarithmic vector fields relative to singular curves

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月14日

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  • Shinichi Tajima,
  • Katsusuke Nabeshima

摘要

Logarithmic vector fields along a singular curve and the Camacho-Sad-Suwa indices, generalizations of the Camacho-Sad index introduced by T. Suwa, are considered in the context of computational complex analysis. An effective algorithm is introduced for computing a basis of the module of germs of logarithmic vector fields along a given singular curve. A new method is described for computing the Camacho-Sad-Suwa indices. The keys of our approach are the use of local cohomology and Grothendieck local duality. Several examples are given for illustration.