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Mirror configurations of points and lines and algebraic surfaces of degree four. / Podkorytov, S. S.

In: Journal of Mathematical Sciences , Vol. 91, No. 6, 01.01.1998, p. 3526-3531.

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

Harvard

Podkorytov, SS 1998, 'Mirror configurations of points and lines and algebraic surfaces of degree four', Journal of Mathematical Sciences , vol. 91, no. 6, pp. 3526-3531. https://doi.org/10.1007/BF02434931

APA

Podkorytov, S. S. (1998). Mirror configurations of points and lines and algebraic surfaces of degree four. Journal of Mathematical Sciences , 91(6), 3526-3531. https://doi.org/10.1007/BF02434931

Vancouver

Podkorytov SS. Mirror configurations of points and lines and algebraic surfaces of degree four. Journal of Mathematical Sciences . 1998 Jan 1;91(6):3526-3531. https://doi.org/10.1007/BF02434931

Author

Podkorytov, S. S. / Mirror configurations of points and lines and algebraic surfaces of degree four. In: Journal of Mathematical Sciences . 1998 ; Vol. 91, No. 6. pp. 3526-3531.

BibTeX

@article{7655945698fb403cab10f0a513b3dc0c,
title = "Mirror configurations of points and lines and algebraic surfaces of degree four",
abstract = "We prove that mirror nonsingular configurations of m points and n lines in ℝP3 exist only for m ≤ 3, n ≡ 0 or 1 (mod 4) and for m = 0 or 1 (mod 4), n ≡ 0 (mod 2). In addition, we give an elementary proof of V. M. Kharlamov's well-known result saying that if a nonsingular surface of degree four in ℝP3 is noncontractible and has M ≥ 5 components, then it is nonmirror. For the cases M = 5, 6, 7, and 8, Kharlamov suggested an elementary proof using an analogy between such surfaces and configurations of M -1 points and a line. Our proof covers the remaining cases M = 9, 10.",
author = "Podkorytov, {S. S.}",
year = "1998",
month = jan,
day = "1",
doi = "10.1007/BF02434931",
language = "English",
volume = "91",
pages = "3526--3531",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Nature",
number = "6",

}

RIS

TY - JOUR

T1 - Mirror configurations of points and lines and algebraic surfaces of degree four

AU - Podkorytov, S. S.

PY - 1998/1/1

Y1 - 1998/1/1

N2 - We prove that mirror nonsingular configurations of m points and n lines in ℝP3 exist only for m ≤ 3, n ≡ 0 or 1 (mod 4) and for m = 0 or 1 (mod 4), n ≡ 0 (mod 2). In addition, we give an elementary proof of V. M. Kharlamov's well-known result saying that if a nonsingular surface of degree four in ℝP3 is noncontractible and has M ≥ 5 components, then it is nonmirror. For the cases M = 5, 6, 7, and 8, Kharlamov suggested an elementary proof using an analogy between such surfaces and configurations of M -1 points and a line. Our proof covers the remaining cases M = 9, 10.

AB - We prove that mirror nonsingular configurations of m points and n lines in ℝP3 exist only for m ≤ 3, n ≡ 0 or 1 (mod 4) and for m = 0 or 1 (mod 4), n ≡ 0 (mod 2). In addition, we give an elementary proof of V. M. Kharlamov's well-known result saying that if a nonsingular surface of degree four in ℝP3 is noncontractible and has M ≥ 5 components, then it is nonmirror. For the cases M = 5, 6, 7, and 8, Kharlamov suggested an elementary proof using an analogy between such surfaces and configurations of M -1 points and a line. Our proof covers the remaining cases M = 9, 10.

UR - http://www.scopus.com/inward/record.url?scp=54749144020&partnerID=8YFLogxK

U2 - 10.1007/BF02434931

DO - 10.1007/BF02434931

M3 - Article

AN - SCOPUS:54749144020

VL - 91

SP - 3526

EP - 3531

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -

ID: 49886766