Fano 4-folds having a prime divisor of Picard number 1 [1]

Abstract.  We will talk about a classification result for smooth,
complex Fano 4-folds of Picard number 3 having a prime divisor of
Picard number 1, and we will see that they form 28 families. We
compute the main numerical invariants, determine the base locus of the
anticanonical divisor, and study their deformations to give an upper
bound of both the dimension of the automorphism group and the
dimension of the base of the Kuranishi family of a general member.
Lastly, we will discuss rationality.