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VOL. 43 | 2010 On Mixed Plane Curves of Polar Degree 1
Mutsuo Oka

Editor(s) Toshizumi Fukui, Adam Harris, Alexander Isaev, Satoshi Koike, Laurentiu Paunescu


Let $f(\mathbf{z, \bar{z}})$ be a mixed strongly polar homogeneous polynomial of 3 variables $z = (z1, z2, z3)$. It defines a Riemann surface $V := \{[\mathbf{z}] \in \mathbb{P}^2 | f(\mathbf{z, \bar{z}) =0\}$ in the complex projective space $\mathbb{P}^2$. We will show that for an arbitrary given $g \geq 0$, there exists a mixed polar homogenous polynomial with polar degree $1$ which defines a projective surface of genus $g$. For the construction, we introduce a new type of weighted homogeneous polynomials which we call polar weighted homogenous polynomials of the twisted join type.


Published: 1 January 2010
First available in Project Euclid: 18 November 2014

zbMATH: 1227.14031
MathSciNet: MR2763237

Rights: Copyright © 2010, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.


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