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- W4289763932 abstract "Let U be the tautological subbundle on the Grassmannian $mathrm{Gr}(k, n)$. There is a natural morphism $mathrm{Tot}(U) to mathbb{A}^n$. Using it, we give a semiorthogonal decomposition for the bounded derived category $D^b_{mathrm{coh}}(mathrm{Tot}(U))$ into several exceptional objects and several copies of $D^b_{mathrm{coh}}(mathbb{A}^n)$. We also prove a global version of this result: given a vector bundle $E$ with a regular section $s$, consider a subvariety of the relative Grassmannian $mathrm{Gr}(k, E)$ of those subspaces which contain the value of $s$. The derived category of this subvariety admits a similar decomposition into copies of the base and the zero locus of $s$. This may be viewed as a generalization of the blow-up formula of Orlov, which is the case $k = 1$." @default.
- W4289763932 created "2022-08-04" @default.
- W4289763932 creator A5052324799 @default.
- W4289763932 date "2018-07-04" @default.
- W4289763932 modified "2023-10-01" @default.
- W4289763932 title "Semiorthogonal decompositions on total spaces of tautological bundles" @default.
- W4289763932 doi "https://doi.org/10.48550/arxiv.1807.01802" @default.
- W4289763932 hasPublicationYear "2018" @default.
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