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Remarks on the algebraic approach to intersection theory

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Abstract

The purpose of this paper is to study the solutions ofr algebraic (homogeneous) equations in projectiven-space counted with multiplicities given by the length of well-defined primary ideals. Hence we need an extension of the algebraic approach to the intersection theory given in [20]. Also, we will prove that our intersection numbers of irreducible components coincide with the multiplicities of the obvious primary ideals in the obvious local ring of the join-variety.

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Authors and Affiliations

  1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, 400 005, Bombay, India

    Dilip P. Patil

  2. Department of Mathematics, Martin-Luther-University, DDR-4010, Halle, German Democratic Republic

    Wolfgang Vogel

Authors
  1. Dilip P. Patil
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  2. Wolfgang Vogel
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To the memory of Wolfgang Gröbner

The second author would like to express his gratitude to the Tata Institute of Fundamental Research and Martin-Luther-University of Halle for its support of his stay at the Tata Institute in Bombay in November–December, 1982. Also, this author would like to thank the School of Mathematics of the Tata Institute for their hospitality during the preparation of this work.

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Patil, D.P., Vogel, W. Remarks on the algebraic approach to intersection theory. Monatshefte für Mathematik 96, 233–250 (1983). https://doi.org/10.1007/BF01605490

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