Pfaffian representations of cubic surfaces

Let be a field of characteristic zero. We describe an algorithm which requires a homogeneous polynomial of degree three in and a zero of in and ensures a linear Pfaffian representation of with entries in , under mild assumptions on and . We use this result to give an explicit construction of (and to...

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Bibliographic Details
Published in:Geometriae dedicata 2014-02, Vol.168 (1), p.69-86
Main Author: Tanturri, Fabio
Format: Article
Language:English
Subjects:
Algebraic Geometry
Convex and Discrete Geometry
Differential Geometry
Hyperbolic Geometry
Mathematics
Mathematics and Statistics
Original Paper
Projective Geometry
Topology
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Description
Summary:Let be a field of characteristic zero. We describe an algorithm which requires a homogeneous polynomial of degree three in and a zero of in and ensures a linear Pfaffian representation of with entries in , under mild assumptions on and . We use this result to give an explicit construction of (and to prove the existence of) a linear Pfaffian representation of , with entries in , being an algebraic extension of of degree at most six. An explicit example of such a construction is given.
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-012-9818-x