Zilber expressed a conjecture for $\aleph_{1}$- categorical theories.(In 80s)

Zilber's Conjecture: The geometry of any $\aleph_{1}$- categorical structure is one of the following:

a) Trivial (No structure)

b) Linear (Locally modular): Vector Spaces.

c) Non-Linear (Non Locally modular): Algebraically Closed Fields(ACF).

In other words Zilber conjectured that any non-locally modular strongly minimal set interprets an ACF.

Hrushovski construct a new class of $\aleph_{1}$- categorical structures, disproving Zilber's conjecture.(A New Strongly Minimal Set - Annals of Pure and Applied Logic 1993 ).

Hrushovski generalized the Frasse's method to construct his counter example.
Hrushovski construct an $\omega$- saturated strongly minimal set whose geometry is *flat*.

**Definition:** A combinatorial geometry J is *flat* if whenever $E_{i}(i\in I)$ are finite number of finite-dimensional closed subset of J, s ranges over the subsets of I, then $\sum_{s}(-1)^{card(s)}\leq0$.

Hrushovski proved the following theorem:

**Theorem:** Let D be a saturated strongly minimal set whose geometry is flat. Then D does not interpret an infinite group. So D does not interpret an ACF.

**Question:** Can we use Hrushovski's method to find a saturated strongly minimal set whose geometry is not flat ?