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Weighted projective spaces admitting $\mathbb Q$-Gorenstein smoothings to Fano threefolds with Picard number one
We study well-formed weighted projective threefolds $X=\mathbb P(w_0,w_1,w_2,w_3)$ that admit a $\mathbb Q$-Gorenstein smoothing to a smooth Fano threefold of Picard number one. For del Pezzo threefolds $V_d$ and prime Fano threefolds $Y_g$, we derive three necessary numerical and local conditions:
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