Résumé
Ashok and Douglas have shown that in finite sequences of type IIB flux vacua with imaginary self-dual flux can only occur in so-called D-limits, corresponding to singular points in complex structure moduli space. In this work we re fine this no-go result by demonstrating that there are no in finite sequences accumulating to the large complex structure point of a certain class of one-parameter Calabi-Yau manifolds. We perform a similar analysis for conifold points and for the decoupling limit, obtaining identical results. Furthermore, we establish the absence of in finite sequences in a D-limit corresponding to the large complex structure limit of a two-parameter Calabi-Yau. In particular, our results demonstrate analytically that the series of vacua recently discovered by Ahlqvist et al., seemingly accumulating to the large complex structure point, are finite. We perform a numerical study of these series close to the large complex structure point using appropriate approximations for the period functions. This analysis reveals that the series bounce out from the large complex structure point, and that the flux eventually ceases to be imaginary self-dual. Finally, we study D-limits for F-theory compactifications on K3 x K3 for which the finiteness of supersymmetric vacua is already established. We do find in finite sequences of flux vacua which are, however, identified by automorphisms of K3.