AdS type vacua, because the determining equations for Minkowski vacua do not depend on the Kähler potential.

Tadpole cancellation and supersymmetry constraints
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The single most interesting aspect of the modified Kähler potential for the axio-dilaton is that unbroken supersymmetry no longer requires the three-form flux to be imaginary self-dual (ISD) even in the absence of non-perturbative corrections. This renders the flux contribution to the tadpole non-positive definite and makes the tadpole cancellation condition less constraining than in the usual cases. This is essentially what allows the existence of the sequence of flux vacua with arbitrarily large flux numbers found in [@wati].

More concretely, using the explicit form of the flux superpotential the supersymmetry constraint for the axio-dilaton reads [^5] $$\eqlabel{dileom} D_\tau W =
-{1\over \tau - \bar \tau}\int (3 G + \bar G)\wedge \Omega = 0,$$ which is solved by $$\eqlabel{dilsolv} \tau = {1\over 2} {W_{RR}\over W_{NS}} \left( 3 -
e^{i \varphi}\right)\qquad {\rm where}\qquad \varphi={\rm Arg}\left(
W_{NS} \over W_{RR}\right).$$ The supersymmetry constraint for the complex structure moduli is expressed in terms of a basis $\chi_i$ of harmonic $(2,1)$ forms $$D_i W = \int G\wedge \chi_i  = 0.$$ From this we see that unbroken supersymmetry requires the Hodge decomposition of 