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Estimates of the number of singular points of a complex hypersurface and related questions. / Ivanov, O. A.; Netsvetaev, N. Yu.

In: Journal of Mathematical Sciences, Vol. 91, No. 6, 01.01.1998, p. 3448-3455.

Research output: Contribution to journal › Article › peer-review

Harvard

Ivanov, OA & Netsvetaev, NY 1998, 'Estimates of the number of singular points of a complex hypersurface and related questions', Journal of Mathematical Sciences, vol. 91, no. 6, pp. 3448-3455. https://doi.org/10.1007/BF02434921

APA

Ivanov, O. A., & Netsvetaev, N. Y. (1998). Estimates of the number of singular points of a complex hypersurface and related questions. Journal of Mathematical Sciences, 91(6), 3448-3455. https://doi.org/10.1007/BF02434921

Vancouver

Ivanov OA, Netsvetaev NY. Estimates of the number of singular points of a complex hypersurface and related questions. Journal of Mathematical Sciences. 1998 Jan 1;91(6):3448-3455. https://doi.org/10.1007/BF02434921

Author

Ivanov, O. A. ; Netsvetaev, N. Yu. / Estimates of the number of singular points of a complex hypersurface and related questions. In: Journal of Mathematical Sciences. 1998 ; Vol. 91, No. 6. pp. 3448-3455.

BibTeX

@article{99fc78d9aebc461b992e928be439d73f,
title = "Estimates of the number of singular points of a complex hypersurface and related questions",
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 bm-1 ± (d) are the inertia indices of the intersection form of a nonsingular hypersurface of degree d in ℂPm, then the inequality Am(d) < mm{b m-1 +(d),bm-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 21 ≤ m ≤ 14, 3 ≤ d ≤ 17 and for 3 ≤ m ≤ 14, d = 18, 19 is given.",
author = "Ivanov, {O. A.} and Netsvetaev, {N. Yu}",
year = "1998",
month = jan,
day = "1",
doi = "10.1007/BF02434921",
language = "English",
volume = "91",
pages = "3448--3455",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Nature",
number = "6",

}

RIS

TY - JOUR

T1 - Estimates of the number of singular points of a complex hypersurface and related questions

AU - Ivanov, O. A.

AU - Netsvetaev, N. Yu

PY - 1998/1/1

Y1 - 1998/1/1

N2 - 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 bm-1 ± (d) are the inertia indices of the intersection form of a nonsingular hypersurface of degree d in ℂPm, then the inequality Am(d) < mm{b m-1 +(d),bm-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 21 ≤ m ≤ 14, 3 ≤ d ≤ 17 and for 3 ≤ m ≤ 14, d = 18, 19 is given.

AB - 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 bm-1 ± (d) are the inertia indices of the intersection form of a nonsingular hypersurface of degree d in ℂPm, then the inequality Am(d) < mm{b m-1 +(d),bm-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 21 ≤ m ≤ 14, 3 ≤ d ≤ 17 and for 3 ≤ m ≤ 14, d = 18, 19 is given.

UR - http://www.scopus.com/inward/record.url?scp=54749136258&partnerID=8YFLogxK

U2 - 10.1007/BF02434921

DO - 10.1007/BF02434921

M3 - Article

AN - SCOPUS:54749136258

VL - 91

SP - 3448

EP - 3455

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -

ID: 36967515