Period integrals of a hypersurface determine an ideal of polynomials, and for algebraic cycles this ideal can be lifted exactly to recover the subvariety's equations, demonstrated by proving Picard numbers 8 and 14 for two quartics.
The genus of space curves
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On reconstructing subvarieties from their periods
Period integrals of a hypersurface determine an ideal of polynomials, and for algebraic cycles this ideal can be lifted exactly to recover the subvariety's equations, demonstrated by proving Picard numbers 8 and 14 for two quartics.