Geodesic
Singular points of complex algebraic hypersurfaces
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 6, pp. 670-679.

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We consider a complex hypersurface $V$ given by an algebraic equation in $k$ unknowns, where the set $ A\subset {\mathbb Z}^k $ of monomial exponents is fixed, and all the coefficients are variable. In other words, we consider a family of hypersurfaces in $ ({\mathbb C \setminus 0}) ^ {k} $ parametrized by its coefficients $a =(a_{\alpha})_{\alpha \in A} \in {\mathbb C} ^{A} $. We prove that when $A$ generates the lattice $\mathbb Z^k$ as a group, then over the set of regular points $a$ in the $A$-discriminantal set, the singular points of $V$ admit a rational expression in $a$.
Keywords: singular point
Mots-clés : $A$-discriminant, logarithmic Gauss map. 
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Irina A. Antipova; Evgeny N. Mikhalkin; Avgust K. Tsikh. Singular points of complex algebraic hypersurfaces. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 6, pp. 670-679. http://geodesic.mathdoc.fr/item/JSFU_2018_11_6_a1/

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