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arXiv · 1712.09091

Binary quartic forms with vanishing $J$-invariant

Stanley Yao Xiao
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Abstract

We obtain an asymptotic formula for the number of $\operatorname{GL}_2(\mathbb{Z})$-equivalence classes of irreducible binary quartic forms with integer coefficients with vanishing $J$-invariant and whose Hessians are proportional to the squares of reducible or positive definite binary quadratic form. These results give a case where one is able to count integral orbits inside a relatively open real orbit of a variety closed under a group action of degree at least three.

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Stanley Yao Xiao. 2017-12-25. Binary quartic forms with vanishing $J$-invariant. https://arxiv.org/abs/1712.09091

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