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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Nonsingular algebraic curves in $ {\bf R}{\rm P}\sp 1\times{\bf R}{\rm P}\sp 1$


Author: Sachiko Matsuoka
Journal: Trans. Amer. Math. Soc. 324 (1991), 87-107
MSC: Primary 14P25; Secondary 57M99
MathSciNet review: 986695
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Abstract: We give some restrictions for the mutual position of the connected components of a nonsingular algebraic curve in the product space $ {\mathbf{R}}{P^1} \times {\mathbf{R}}{P^1}$ of two real projective lines. We obtain our main theorem by calculating the Brown invariant of a certain quadratic form determined by the algebraic curve. Moreover, we consider a double covering of $ {\mathbf{C}}{P^1} \times {\mathbf{C}}{P^1}$ branched along the complexification of our curve and antiholomorphic involutions that are the lifts of the complex conjugation.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1991-0986695-1
PII: S 0002-9947(1991)0986695-1
Keywords: Algebraic curve, complex conjugation, signature, Brown invariant, branched double covering
Article copyright: © Copyright 1991 American Mathematical Society