### Abstract

We determine the values attained by the rank of the Gauss map of a projective model for a fixed algebraic variety in positive characteristic p. In particular, it is shown that any variety in p > 0 has a projective model such that the differential of the Gauss map is identically zero. On the other hand, we prove that there exists a product of two or more projective spaces admitting an embedding into a projective space such that the differential of the Gauss map is identically zero if and only if p = 2.

Original language | English |
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Pages (from-to) | 297-300 |

Number of pages | 4 |

Journal | Journal of Pure and Applied Algebra |

Volume | 214 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2010 Mar |

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### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

**Any algebraic variety in positive characteristic admits a projective model with an inseparable Gauss map.** / Fukasawa, Satoru; Kaji, Hajime.

Research output: Contribution to journal › Article

*Journal of Pure and Applied Algebra*, vol. 214, no. 3, pp. 297-300. https://doi.org/10.1016/j.jpaa.2009.05.007

}

TY - JOUR

T1 - Any algebraic variety in positive characteristic admits a projective model with an inseparable Gauss map

AU - Fukasawa, Satoru

AU - Kaji, Hajime

PY - 2010/3

Y1 - 2010/3

N2 - We determine the values attained by the rank of the Gauss map of a projective model for a fixed algebraic variety in positive characteristic p. In particular, it is shown that any variety in p > 0 has a projective model such that the differential of the Gauss map is identically zero. On the other hand, we prove that there exists a product of two or more projective spaces admitting an embedding into a projective space such that the differential of the Gauss map is identically zero if and only if p = 2.

AB - We determine the values attained by the rank of the Gauss map of a projective model for a fixed algebraic variety in positive characteristic p. In particular, it is shown that any variety in p > 0 has a projective model such that the differential of the Gauss map is identically zero. On the other hand, we prove that there exists a product of two or more projective spaces admitting an embedding into a projective space such that the differential of the Gauss map is identically zero if and only if p = 2.

UR - http://www.scopus.com/inward/record.url?scp=70350287775&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70350287775&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2009.05.007

DO - 10.1016/j.jpaa.2009.05.007

M3 - Article

AN - SCOPUS:70350287775

VL - 214

SP - 297

EP - 300

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 3

ER -