### 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 |
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Pages (from-to) | 1-15 |

Number of pages | 15 |

Journal | Communications in Algebra |

DOIs | |

Publication status | Accepted/In press - 2018 Feb 27 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

**Higher Gauss maps of Veronese varieties—A generalization of Boole’s formula and degree bounds for higher Gauss map images.** / Kaji, Hajime.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Higher Gauss maps of Veronese varieties—A generalization of Boole’s formula and degree bounds for higher Gauss map images

AU - Kaji, Hajime

PY - 2018/2/27

Y1 - 2018/2/27

N2 - 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.

AB - 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.

KW - Boole’s formula

KW - degree bound

KW - dual variety

KW - higher Gauss map

KW - Veronese variety

UR - http://www.scopus.com/inward/record.url?scp=85042940550&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85042940550&partnerID=8YFLogxK

U2 - 10.1080/00927872.2018.1435790

DO - 10.1080/00927872.2018.1435790

M3 - Article

AN - SCOPUS:85042940550

SP - 1

EP - 15

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

ER -