Varieties with degenerate dual variety

In this article we face the problem of classification of smooth complex pro jective varieties with degenerate dual variety (also called positive defect varieties). We give a description of the structure of the normal bundle to the general contact locus in the variety. We characterize some particular varieties with degenerate dual variety in terms of this bundle: scrolls, hy perplane sections of positive defect varieties and products. We also prove some results of extendability of positive defect varieties. Finally, we ans wer two questions posed in [2] about the existence of some positive defect Fano varieties.