I am reading these notes of an excellent course by Kuznetsov on Homological Projective Duality. On page 10 there is Example 1''.

One starts with projective space, endowed with the identity embedding in itself and the slightly tweaked Lefschetz decomposition $A_0 = <\mathcal{O},\mathcal{O}(1),\mathcal{O}(2)>$, $A_{i} = <\mathcal{O}(2)>$. It is stated that the HP-dual of this is a non-commutative space, actually a fibration in non-commutative projective lines. It's not obvious to me why this space cannot be realised geometrically, say by a space $Y$, perhaps together with a sheaf of algebras over it.

So my question is: why can't we find a dual of geometric origin?