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arXiv · 1210.1763

Pfaffian bundles on cubic surfaces and configurations of planes

Frederic Han
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Abstract

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 $P_5$. Applications to the geometry of Palatini threefolds and Debarre-Voisin's Hyper-K\"ahler manifolds are also discussed.

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Frederic Han. 2012-10-05. Pfaffian bundles on cubic surfaces and configurations of planes. https://arxiv.org/abs/1210.1763

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