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Geometry of Factorization Identities for Discriminants

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Abstract

Let Δn be the discriminant of a general polynomial of degree n and \(\mathcal{N}\) be the Newton polytope of Δn. We give a geometric proof of the fact that the truncations of Δn to faces of \(\mathcal{N}\) are equal to products of discriminants of lesser n degrees. The proof is based on the blow-up property of the logarithmic Gauss map for the zero set of Δn.

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Funding

This work was supported by Krasnoyarsk Mathematical Center financed by the Ministry of Science and Higher Education of the Russian Federation in the context of the creation and development of regional scientific and educational mathematical centers, agreement 075-02-2020-1534/1.

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Authors and Affiliations

  1. Siberian Federal University, 660041, Krasnoyarsk, Russia

    E. N. Mikhalkin, V. A. Stepanenko & A. K. Tsikh

Authors
  1. E. N. Mikhalkin
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  2. V. A. Stepanenko
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  3. A. K. Tsikh
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Correspondence to E. N. Mikhalkin, V. A. Stepanenko or A. K. Tsikh.

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Translated by I. Ruzanova

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Mikhalkin, E.N., Stepanenko, V.A. & Tsikh, A.K. Geometry of Factorization Identities for Discriminants. Dokl. Math. 102, 279–282 (2020). https://doi.org/10.1134/S1064562420040134

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  • DOI: https://doi.org/10.1134/S1064562420040134

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