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Journal of Siberian Federal University. Mathematics & Physics, 2018, Volume 11, Issue 6, Pages 670–679
DOI: https://doi.org/10.17516/1997-1397-2018-11-6-670-679
(Mi jsfu712)
 

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
Full-text PDF (130 kB) Citations (1)
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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.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.2604.2017/PCh
14.Y26.31.0006
Russian Foundation for Basic Research 18-51-41011_Uzb_t
The first two authors were supported by the grant of Ministry of Education and Science of the Russian Federation (no. 1.2604.2017/PCh). The third author was supported by the grant of the Russian Federation Government for scientific research under the supervision of leading scientists at Siberian Federal University (no. 14.Y26.31.0006) and grant RFBR, no. 18-51-41011 Uzb.
Received: 03.09.2018
Received in revised form: 22.10.2018
Accepted: 28.10.2018
Bibliographic databases:
Document Type: Article
UDC: 517.55
Language: English
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
Citation in format AMSBIB
\Bibitem{AntMikTsi18}
\by Irina~A.~Antipova, Evgeny~N.~Mikhalkin, Avgust~K.~Tsikh
\paper Singular points of complex algebraic hypersurfaces
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2018
\vol 11
\issue 6
\pages 670--679
\mathnet{http://mi.mathnet.ru/jsfu712}
\crossref{https://doi.org/10.17516/1997-1397-2018-11-6-670-679}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000452216700002}
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  • This publication is cited in the following 1 articles:
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    Журнал Сибирского федерального университета. Серия "Математика и физика"
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