C. Ciliberto et al., CLASSIFICATION OF VARIETIES WITH CANONICAL CURVE SECTION VIA GAUSSIANMAPS ON CANONICAL CURVES, American journal of mathematics, 120(1), 1998, pp. 1-21
The purpose of this article is to develop further a method to classify
varieties X subset of P-N having canonical curve section, using Gauss
ian map computations. In a previous article we applied these technique
s to classify prime Fano threefolds, that is Fano threefolds whose Pic
ard group is generated by the hyperplane bundle. In this article we ex
tend this method and classify Fano threefolds of higher index and Muka
i varieties, i.e., varieties of dimension four or more with canonical
curve sections. First we determine when the Hilbert scheme Ht of such
varieties X is nonempty. Moreover, in the case of Picard number one, w
e prove that H is irreducible and that the examples of Fano-Iskovskih
and Mukai form a dense open subset of smooth points of H.