Divisor topologies of CICY 3-folds and their applications to phenomenology

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In this article, we present a classification for the divisor topologies of the projective complete intersection Calabi-Yau (pCICY) 3-folds realized as hypersurfaces in the product of complex projective spaces.

• There are 7890 such pCICYs of which 7820 are favorable, and can be subsequently useful for phenomenological purposes.
• To our surprise we find that the whole pCICY database results in only 11 (so-called coordinate) divisors $(D)$ of distinct topology and we classify those surfaces with their possible deformations inside the pCICY 3-fold, which turn out to be satisfying $1 \leq h^{2,0}(D) \leq 7$.
• We also present a classification of the so-called ample divisors for all the favorable pCICYs which can be useful for fixing all the (saxionic) K\"ahler moduli through a single non-perturbative term in the superpotential.