Stability and certain \(\mathbb{P}^n\)-functors. (English) Zbl 1531.14028
Summary: Let \(X\) be a \(K3\) surface. We prove that Addington’s \(\mathbb{P}^n\)-functor between the derived categories of \(X\) and the Hilbert scheme of points \(X^{[k]}\) maps stable vector bundles on \(X\) to stable vector bundles on \(X^{[k]}\), given some numerical conditions are satisfied.
MSC:
| 14F08 | Derived categories of sheaves, dg categories, and related constructions in algebraic geometry |
| 14J28 | \(K3\) surfaces and Enriques surfaces |
| 14J60 | Vector bundles on surfaces and higher-dimensional varieties, and their moduli |
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