Geodesic
Singular strata of cuspidal type for the classical discriminant
Sbornik. Mathematics, Tome 206 (2015) no. 2, pp. 282-310 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider an algebraic equation with variable complex coefficients. For the reduced discriminant set of such an equation we obtain parametrizations of the singular strata corresponding to the existence of roots of multiplicity at least $j$. These parametrizations are the restrictions of the Horn-Kapranov parametrization of the whole discriminant set to a chain of nested linear subspaces of the projective space. It is proved that such strata can be transformed into reduced $A$-discriminant sets by monomial transformations. Bibliography: 12 titles.
Keywords: general algebraic equation, Horn-Kapranov parametrization, singular stratum.
Mots-clés : $A$-discriminant set 
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E. N. Mikhalkin; A. K. Tsikh. Singular strata of cuspidal type for the classical discriminant. Sbornik. Mathematics, Tome 206 (2015) no. 2, pp. 282-310. http://geodesic.mathdoc.fr/item/SM_2015_206_2_a5/

[1] I. M. Gelfand, M. M. Kapranov, A. V. Zelevinsky, Discriminants, resultants, and multidimensional determinants, Math. Theory Appl., Birkhäuser Boston, Inc., Boston, MA, 1994, x+523 pp. | DOI | MR | Zbl

[2] M. M. Kapranov, “A characterization of $A$-discriminantal hypersurfaces in terms of the logarithmic Gauss map”, Math. Ann., 290:1 (1991), 277–285 | DOI | MR | Zbl

[3] Algebraic statistics for computational biology, eds. L. Pachter, B. Sturmfels, Cambridge Univ. Press, New York, 2005, xii+420 pp. | DOI | MR | Zbl

[4] B. Sturmfels, “Open problems in algebraic statistics”, Emerging applications of algebraic geometry, IMA Vol. Math. Appl., 149, Springer, New York, 2009, 351–363 | DOI | MR | Zbl

[5] J. Huh, Discriminants, Horn uniformization, and varieties with maximum likelihood degree one, arXiv: 1301.2732v2

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

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

[8] I. A. Antipova, E. N. Mikhalkin, “Analytic continuations of a general algebraic function by means of Puiseux series”, Proc. Steklov Inst. Math., 279:1 (2012), 3–13 | DOI | MR | Zbl

[9] M. Passare, A. Tsikh, “Amoebas: their spines and their contours”, Idempotent mathematics and mathematical physics, Contemp. Math., 377, Amer. Math. Soc., Providence, RI, 2005, 275–288 | DOI | MR | Zbl

[10] G. Mikhalkin, “Real algebraic curves, the moment map and amoebas”, Ann. of Math. (2), 151:1 (2000), 309–326 | DOI | MR | Zbl

[11] N. A. Bushueva, A. K. Tsikh, “On amoebas of algebraic sets of higher codimension”, Proc. Steklov Inst. Math., 279:1 (2012), 52–63 | DOI | MR | Zbl

[12] I. A. Antipova, “Inversion of many-dimensional Mellin transforms and solutions of algebraic equations”, Sb. Math., 198:4 (2007), 447–463 | DOI | DOI | MR | Zbl