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Working paper

Two rational nodal quartic threefolds

We prove that the quartic threefolds defined by ∑_{i=0}^5 x_i=∑_{i=0}^5 x^4_i−t(∑_{i=0}^5 x^2_i)^2=0 in ℙ5 are rational for t=1/6 and t=7/10.