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Rationality of fields of invariants for some representations of SL2 × SL2

Part of: Curves Birational geometry Algebraic groups

Published online by Cambridge University Press:  22 May 2013

Shouhei Ma
Shouhei Ma*
Affiliation:
Graduate School of Mathematics, Nagoya University, Nagoya 464-8601, Japan email ma@math.nagoya-u.ac.jp
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Abstract

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We prove that the quotient by ${\mathrm{SL} }_{2} \times {\mathrm{SL} }_{2} $ of the space of bidegree $(a, b)$ curves on ${ \mathbb{P} }^{1} \times { \mathbb{P} }^{1} $ is rational when $ab$ is even and $a\not = b$.

Keywords

SL2 × SL2-representationrationality problemrational space curvetransvectant for biform

MSC classification

Secondary: 14L30: Group actions on varieties or schemes (quotients) 14E08: Rationality questions 14H50: Plane and space curves
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 7 , July 2013 , pp. 1225 - 1234
Copyright
© The Author(s) 2013 

References

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