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Rationality of fields of invariants for some representations of SL2 × SL2
- Part of
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- Journal:
- Compositio Mathematica / Volume 149 / Issue 7 / July 2013
- Published online by Cambridge University Press:
- 22 May 2013, pp. 1225-1234
- Print publication:
- July 2013
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- Article
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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 
$a\not = b$.
