Pfaffian representations of cubic surfaces

Fabio Tanturri (1)

1 SISSA / ISAS - Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies

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.

Domaines: Géométrie algébrique [math.AG]

Fabio Tanturri. Pfaffian representations of cubic surfaces. Geometriae Dedicata, 2014, 1 ; 168, pp.69-86. ⟨10.1007/s10711-012-9818-x⟩. ⟨hal-01263517⟩