Innovations in Incidence Geometry

A remark on Grassmann and Veronese embeddings of $\mathbb P^3$ in characteristic 2

Ogül Arslan and Peter Sin

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Abstract

We answer a question raised in a recent paper by I. Cardinali and A. Pasini. Over an algebraically closed field of characteristic 2, we show that a certain projection of 9 to 8 induces an isomorphism of algebraic varieties from the quadratic Veronese embedding of 3 to the standard embedding of the orthogonal Grassmanian of lines of a quadric in 4.

Article information

Source
Innov. Incidence Geom., Volume 14, Number 1 (2015), 111-117.

Dates
Received: 9 September 2014
Accepted: 20 March 2015
First available in Project Euclid: 28 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.iig/1551323031

Digital Object Identifier
doi:10.2140/iig.2015.14.111

Mathematical Reviews number (MathSciNet)
MR3450954

Zentralblatt MATH identifier
1333.51001

Subjects
Primary: 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35] 20G15: Linear algebraic groups over arbitrary fields 51B25: Lie geometries

Keywords
Grassmann embedding Veronese embedding morphisms Klein quadric Plücker coordinates

Citation

Arslan, Ogül; Sin, Peter. A remark on Grassmann and Veronese embeddings of $\mathbb P^3$ in characteristic 2. Innov. Incidence Geom. 14 (2015), no. 1, 111--117. doi:10.2140/iig.2015.14.111. https://projecteuclid.org/euclid.iig/1551323031


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