Higher Gauss maps of Veronese varieties—A generalization of Boole’s formula and degree bounds for higher Gauss map images

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Abstract

The image of the higher Gauss map for a projective variety is discussed. The notion of higher Gauss maps here was introduced by Fyodor L. Zak as a generalization of both ordinary Gauss maps and conormal maps. The main result is a closed formula for the degree of those images of Veronese varieties. This yields a generalization of a classical formula by George Boole on the degree of the dual varieties of Veronese varieties in 1844. As an application of our formula, degree bounds for higher Gauss map images of Veronese varieties are given.

Original language English 1-15 15 Communications in Algebra https://doi.org/10.1080/00927872.2018.1435790 Accepted/In press - 2018 Feb 27

Keywords

• Boole’s formula
• degree bound
• dual variety
• higher Gauss map
• Veronese variety

ASJC Scopus subject areas

• Algebra and Number Theory