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The image of the higher Gauss map for a projective variety is discussed. Thenotion of higher Gauss maps here was introduced by Fyodor L. Zak as ageneralization of both ordinary Gauss maps and conormal maps. The main resultis a closed formula for the degree of those images of Veronese varieties. Thisyields a generalization of a classical formula by George Boole on the degree ofthe dual varieties of Veronese varieties in 1844. As an application of ourformula, degree bounds for higher Gauss map images of Veronese varieties aregiven.

Higher Gauss Maps of Veronese Varieties---a generalization of Boole's formula and degree bounds for higher Gauss map images---