|
Zapiski Nauchnykh Seminarov POMI, 1995, Volume 231, Pages 299–308
(Mi znsl3758)
|
|
|
|
Topological methods in geometry
Mirror configurations of points and lines and algebraic surfaces of degree four
S. S. Podkorytov Saint-Petersburg State University
Abstract:
We prove that mirror nonsingular configurations of m points and $n$ lines in $\mathbb RP^3$ exist only for $m\le3$, $n\equiv0$ or $1\pmod4$ and for $m=0$ or $1\pmod4$, $n\equiv0\pmod2$. 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 $\mathbb RP^3$ is noncontractible and has $M\ge5$ 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 $M=9,10$. Bibl. 5 titles.
Received: 07.10.1995
Citation:
S. S. Podkorytov, “Mirror configurations of points and lines and algebraic surfaces of degree four”, Investigations in topology. Part 8, Zap. Nauchn. Sem. POMI, 231, POMI, St. Petersburg, 1995, 299–308; J. Math. Sci. (New York), 91:6 (1998), 3526–3531
Linking options:
https://www.mathnet.ru/eng/znsl3758 https://www.mathnet.ru/eng/znsl/v231/p299
|
Statistics & downloads: |
Abstract page: | 133 | Full-text PDF : | 54 |
|