TY - JOUR

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

AU - Fukasawa, Satoru

AU - Kaji, Hajime

N1 - Funding Information:
The first author was supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists.

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.

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U2 - 10.1016/j.jpaa.2009.05.007

DO - 10.1016/j.jpaa.2009.05.007

M3 - Article

AN - SCOPUS:70350287775

SN - 0022-4049

VL - 214

SP - 297

EP - 300

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 3

ER -