Algebraic curves in $\textbf {R}\textrm {P}(1)\times \textbf {R}\textrm {P}(1)$
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- by Patrick Gilmer PDF
- Proc. Amer. Math. Soc. 113 (1991), 47-52 Request permission
Abstract:
We derive the analogs for curves in $RP(1) \times RP(1)$ of Fiedler’s congruence for curves in $RP(2)$. We also prove a result on the complex orientations of dividing curves in $RP(1) \times RP(1)$.References
- Edgar H. Brown Jr., Generalizations of the Kervaire invariant, Ann. of Math. (2) 95 (1972), 368–383. MR 293642, DOI 10.2307/1970804
- T. Fidler, New congruences in the topology of real plane algebraic curves, Dokl. Akad. Nauk SSSR 270 (1983), no. 1, 56–58 (Russian). MR 705196
- Lucien Guillou and Alexis Marin, Une extension d’un théorème de Rohlin sur la signature, C. R. Acad. Sci. Paris Sér. A-B 285 (1977), no. 3, A95–A98. MR 440566
- Alexis Marin, Quelques remarques sur les courbes algébriques planes réelles, Seminar on Real Algebraic Geometry (Paris, 1977/1978 and Paris, 1978/1979) Publ. Math. Univ. Paris VII, vol. 9, Univ. Paris VII, Paris, 1980, pp. 51–68 (French). MR 700836
- Sachiko Matsuoka, Nonsingular algebraic curves in $\textbf {R}\textrm {P}^1\times \textbf {R}\textrm {P}^1$, Trans. Amer. Math. Soc. 324 (1991), no. 1, 87–107. MR 986695, DOI 10.1090/S0002-9947-1991-0986695-1 —, The configurations of the $M$-curves of degree (4,4) in $R{P^1} \times R{P^1}$ and periods of real $K3$ surfaces, Hokkaido Math. J. 19 (1990), 359-376.
- V. A. Rohlin, Complex orientation of real algebraic curves, Funkcional. Anal. i Priložen. 8 (1974), no. 4, 71–75 (Russian). MR 0368044
- O. Ya. Viro, Achievements in the topology of real algebraic varieties in the last six years, Uspekhi Mat. Nauk 41 (1986), no. 3(249), 45–67, 240 (Russian). MR 854239
- George Wilson, Hilbert’s sixteenth problem, Topology 17 (1978), no. 1, 53–73. MR 498591, DOI 10.1016/0040-9383(78)90012-5
- V. I. Zvonilov, Complex topological characteristics of real algebraic curves on a surface, Funktsional. Anal. i Prilozhen. 16 (1982), no. 3, 56–57 (Russian). MR 674013 —, Complex orientations of real algebraic curves with singularities, Soviet Math. Dokl. 27 (1983), 14-17.
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 113 (1991), 47-52
- MSC: Primary 14P25; Secondary 14G27, 57M99
- DOI: https://doi.org/10.1090/S0002-9939-1991-1062388-5
- MathSciNet review: 1062388