Geodesic
Estimates of the number of singular points of a~complex hypersurface and related questions
Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part 8, Tome 231 (1995), pp. 180-190

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It is well known that the number of isolated singular points of a hypersurface of degree $d$ in $\mathbb CP^m$ does not exceed the Arnol'd number $A_m(d)$, which is defined in combinatorial terms. In the paper it is proved that if $b^\pm_{m-1}(d)$ are the inertia indices of the intersection form of a nonsingular hypersurface of degree $d$ in $\mathbb CP^m$, then the inequality $A_m(d)\min\{b^+_{m-1}(d),b^-_{m-1}(d)\}$ holds if and only if $(m-5)(d-2)\ge18$ and $(m,d)\ne(7,12)$. The table of the Arnol'd numbers for $3\le m\le14$, $3\le d\le17$ and for $3\le m\le8$, $d=18,19$ is given. Bibl. 6 titles. 
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     author = {O. A. Ivanov and N. Yu. Netsvetaev},
     title = {Estimates of the number of singular points of a~complex hypersurface and related questions},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_1995_231_a10/}
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O. A. Ivanov; N. Yu. Netsvetaev. Estimates of the number of singular points of a~complex hypersurface and related questions. Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part 8, Tome 231 (1995), pp. 180-190. http://geodesic.mathdoc.fr/item/ZNSL_1995_231_a10/