## Arkiv för Matematik

### The injectivity of the extended Gauss map of general projections of smooth projective varieties

Marc Coppens

#### Abstract

Let X be a smooth n-dimensional projective variety embedded in some projective space ℙN over the field ℂ of the complex numbers. Associated with the general projection of X to a space ℙN-m (N-m> n+1) one defines an extended Gauss map $\overline{\gamma}\colon\overline{X}\rightarrow\text{Gr}(n;N-m)$ (in case N-m>2n-1 this is the Gauss map of the image of X under the projection). We prove that $\overline{X}$ is smooth. In case any two different points of X do have disjoint tangent spaces then we prove that $\overline{\gamma}$ is injective.

#### Article information

Source
Ark. Mat., Volume 46, Number 1 (2008), 31-41.

Dates
First available in Project Euclid: 31 January 2017

https://projecteuclid.org/euclid.afm/1485907022

Digital Object Identifier
doi:10.1007/s11512-007-0058-5

Mathematical Reviews number (MathSciNet)
MR2379682

Zentralblatt MATH identifier
1142.14317

Rights

#### Citation

Coppens, Marc. The injectivity of the extended Gauss map of general projections of smooth projective varieties. Ark. Mat. 46 (2008), no. 1, 31--41. doi:10.1007/s11512-007-0058-5. https://projecteuclid.org/euclid.afm/1485907022

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