A Mukai pair (X,E) of dimension n and rank r consists of a Fano n-fold X and an ample r-bundle E on X which satisfies the condition c_1(X) = c_1(E).
Such pairs were introduced by S. Mukai in 1988, and have been completely classified when r > n-2 by several authors.
Also, the classification in the case r=n-2 has been almost completed recently, but, for one case, the classification was incomplete.
In this talk, we will focus on this remaining case, and give the complete classification.
Namely, we will provide the classification of Mukai pairs of dimension 4 and rank 2 whose base manifold X has Picard number one.