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This article is cited in 1 scientific paper (total in 1 paper)
Singular points of complex algebraic hypersurfaces
Irina A. Antipovaa, Evgeny N. Mikhalkinb, Avgust K. Tsikhb a Institute of Space and Information Technologies, Siberian Federal University, Kirensky, 26, Krasnoyarsk, 660074, Russia
b Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia
Abstract:
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, $A$-discriminant, logarithmic Gauss map.
Received: 03.09.2018 Received in revised form: 22.10.2018 Accepted: 28.10.2018
Citation:
Irina A. Antipova, Evgeny N. Mikhalkin, Avgust K. Tsikh, “Singular points of complex algebraic hypersurfaces”, J. Sib. Fed. Univ. Math. Phys., 11:6 (2018), 670–679
Linking options:
https://www.mathnet.ru/eng/jsfu712 https://www.mathnet.ru/eng/jsfu/v11/i6/p670
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