Pfaffian representations of cubic surfaces

作者：Tanturri Fabio^*

来源：Geometriae Dedicata, 2014, 168(1): 69-86.

DOI：10.1007/s10711-012-9818-x

• Pfaffian representations
• Cubic surfaces
• ACM sheaves
• Determinantal varieties

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.

• 出版日期2014-2