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Reconstruction of curves from their theta hyperplanes in genera $6$ and $7$
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classification
math.AG
keywords
generagenerichyperplanesthetaargumentcanonicalcertifiedcomplete
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abstract
We derive a formula for reconstructing a generic complex canonical curve $C$ of genus 6 and 7 in terms of the theta hyperplanes of $C$. Hence, we get a generic inverse to the Torelli map, as well as a complete description of the Schottky locus in these genera. The computational part of the proof relies on a certified numerical argument.
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