A survey of the Torelli locus and Newton polygons that corrects a previously erroneous genus computation and thereby proves new infinite families of supersingular curves of genus δp(p−1)/2.
Equations of genus $4$ curves from their theta constants
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abstract
In this article we give explicit formulas for the equations of a generic genus $4$ curve in terms of its theta constants. The method uses the Prym construction and the beautiful classical geometry around it.
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The Torelli locus and Newton polygons
A survey of the Torelli locus and Newton polygons that corrects a previously erroneous genus computation and thereby proves new infinite families of supersingular curves of genus δp(p−1)/2.