Classification of varieties with canonical curve section via Gaussian maps on canonical curves

Rick Miranda, Ciro Ciliberto, Angelo Felice Lopez
1998 American Journal of Mathematics  
The purpose of this article is to further develop a method to classify varieties X ⊂ IP N having canonical curve section, using Gaussian map computations. In a previous article we applied these techniques to classify prime Fano threefolds, that is Fano threefolds whose Picard group is generated by the hyperplane bundle. In this article we extend this method and classify Fano threefolds of higher index and Mukai varieties, i.e. varieties of dimension four or more with canonical curve sections.
more » ... l curve sections. First we determine when the Hilbert scheme H of such varieties X is non empty. Moreover, in the case of Picard number one, we prove that H is irreducible and that the examples of Fano-Iskovskih and Mukai form a dense open subset of smooth points of H.
doi:10.1353/ajm.1998.0001 fatcat:oudyuqhodze4temp4roz6fwgtq