Polynomial time deterministic identity testing algorithm for Σ[3]ΠΣΠ[2] circuits via Edelstein-Kelly type theorem for quadratic polynomials

In this work we resolve conjectures of Beecken, Mitmann and Saxena [BMS13] and Gupta [Gup14], by proving an analog of a theorem of Edelstein and Kelly for quadratic polynomials. As immediate corollary we obtain the first deterministic polynomial time black-box algorithm for testing zeroness of Σ [3] ΠΣΠ [2] circuits.