Abstract
It is well known that the number of isolated singular points of a hypersurface of degree d in ℂPm does not exceed the Arnol’d number Am(d), which is defined in combinatorial terms. In the paper it is proved that if b ±m−1 (d) are the inertia indices of the intersection form of a nonsingular hypersurface of degree d in ℂPm, then the inequality Am(d)<min{b +m−1 (d), b −m−1 (d)} holds if and only if (m−5)(d−2)≥18 and (m,d)≠(7,12). The table of the Arnol’d numbers for 3≤m≤14, 3≤d≤17 and for 3≤m≤14, d=18, 19 is given. Bibliography: 6 titles.
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References
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Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 180–190.
Translated by O. A. Ivanov and N. Yu. Netsvetev.
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Ivanov, O.A., Netsvetaev, N.Y. Estimates of the number of singular points of a complex hypersurface and related questions. J Math Sci 91, 3448–3455 (1998). https://doi.org/10.1007/BF02434921
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DOI: https://doi.org/10.1007/BF02434921