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arXiv · 1203.0999

Pfaffian representations of cubic surfaces

Fabio Tanturri
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Abstract

Let K be a field of characteristic zero. We describe an algorithm which requires a homogeneous polynomial F of degree three in K[x_0,x_1,x_2,x_3] and a zero A of F in P^3_K and ensures a linear pfaffian representation of V(F) with entries in K[x_0,x_1,x_2,x_3], under mild assumptions on F and A. We use this result to give an explicit construction of (and to prove the existence of) a linear pfaffian representation of V(F), with entries in K'[x_0,x_1,x_2,x_3], being K' an algebraic extension of K of degree at most six. An explicit example of such a construction is given.

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Fabio Tanturri. 2014-02-04. Pfaffian representations of cubic surfaces. https://doi.org/10.1007/s10711-012-9818-x

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