Deformations of Isolated Even Double Points of Corank One
نویسنده
چکیده
We give a local deformation theoretic proof of Farkas’ conjecture that a principally polarized complex abelian variety of dimension 4 whose theta divisor has an isolated double point of rank 3 at a point of order two is a Jacobian. The argument yields an explicit local normal form for the theta function near such a point. The proof depends only on the facts that the theta function is even, a general theta divisor is smooth, and a general singular theta divisor has only ordinary singularities.
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