Abstract

The purpose of this article is to develop further a method to classify varieties X ⊂ [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] 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. First we determine when the Hilbert scheme [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /] of such varieties X is nonempty. Moreover, in the case of Picard number one, we prove that [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="03i" /] is irreducible and that the examples of Fano-Iskovskih and Mukai form a dense open subset of smooth points of [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="04i" /].

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1-21
Launched on MUSE
1998-02-01
Open Access
No
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