arXiv · alg-geom/9504007
We compute the Donaldson numbers $q_{17}(CP^2)=2540$ and $q_{21}(CP^2)=233208$.
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Geir Ellingsrud, Joseph Le Potier, Stein A. Stromme. 1995-04-13. Some Donaldson invariants of CP^2. https://arxiv.org/abs/alg-geom/9504007
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Let $C \subset P^{g-1}$ be a smooth canonical curve of genus $g \geq 3$. The purpose of this article is to further develop a method to classify varieties having $C$ as their curve section, using Gaussian map computations. In a previous article a careful analysis of the degeneration to the cone over the hyperplane section was made for _prime_ Fano threefolds, that is Fano threefolds whose Picard group is generated by the hyperplane bundle. In this article we extend this method and classify Fano threefolds of higher index (which still have Picard number one). We are also able to classify Mukai varieties, i.e. varieties of dimension four or more with canonical curve sections.
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I give a way to construct moduli spaces of complexes, as quotients of open subsets of the space of all complexes by the product of the groups of automorphisms of the terms.