2012/10/05 by Frédéric Han, Frederic Han, Han, Frederic · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometry and complex manifolds #math.AG #msc:14J60
paper · pdf · doi:10.48550/arxiv.1210.1763
minor changes: add references
arxiv created 2013/04/20 · arxiv updated 2013/04/23
We give a canonical birational map between the moduli space of pfaffian vector bundles on a cubic surface and the space of complete pentahedra inscribed in the cubic surface. The universal situation is also considered, and we obtain a rationality result. As a by-product, we provide an explicit normal form for five general lines in P5. Applications to the geometry of Palatini threefolds and Debarre-Voisin's Hyper-Kähler manifolds are also discussed.