Geodesic
Detailed factorization identities for classical discriminant
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 1, pp. 23-28.

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A general polynomial in one variable is considered and the explicit factorization formulas for the truncations of the discriminant with respect to coordinate faces of the polynomial Newton polytope are presented. As a result, the extension of the formulas presented by Gelfand–Kapranov–Zelevinsky is obtained.
Keywords: Newton polytope, Horn–Kapranov parametrization.
Mots-clés : discriminant 
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Evgeny N. Mikhalkin; Mearajuddin Nikzad; Vitaly A. Stepanenko. Detailed factorization identities for classical discriminant. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 1, pp. 23-28. http://geodesic.mathdoc.fr/item/JSFU_2022_15_1_a3/

[1] I.Gelfand, M.Kapranov, A.Zelevinsky, Discriminants, resultants and multidimensional determinants, Birkhäuser, Boston, 1994 | MR | Zbl

[2] V.A.Vassiliev, Topology of complements to discriminants, M., 1997 (in Russian) | MR

[3] I.A.Antipova, A.K.Tsikh, “The discriminant locus of a sistem of $n$ Laurent polynomials in $n$ variables”, Izv. Math., 76:5 (2012), 881–906 | DOI | MR | Zbl

[4] E.N.Mikhalkin, V.A.Stepanenko, A.K.Tsikh, “Geometry of factorization identities for discriminants”, Dokl. Math., 102:1 (2020), 279–282 | DOI | Zbl

[5] E.N.Mikhalkin, V.A.Stepanenko, A.K.Tsikh, “Blow-ups for the Horn-Kapranov parametrization of the classical discriminant”, Journ. of the European Math. Society (to appear) | MR

[6] M.Passare, A.Tsikh, “Algebraic equations and hypergeometric series”, The legacy of Niels Henrik Abel, Springer, Berlin–Heidelberg–New York, 2004, 653–672 | DOI | MR | Zbl

[7] A.G.Kurosh, Kurs vysshey algebry, St.-Petersburg, 2020 (in Russian) | MR

[8] V.V.Prasolov, Mnogochleny, M., 2014 (in Russian)